ELECTRICITY CHAPTER # 16 Physics 10th - Question Answers

 Physics 10th - Question Answers

ELECTRICITY
CHAPTER # 16

Q.1: What do you know about the electrical nature of matter?

Ans:
Matter is made up of atoms and an atom consists of three elementary particles called neutron, proton, and electron.

• Proton is positively charged and present in the nucleus. It is 1836 times heavier than an electron.
• Neutron has no charge. It is also present in the nucleus. Its mass is equal to the mass of a proton.
• Electron is a negatively charged particle. Its charge is equal to the charge of a proton. Electrons move around the nucleus in orbits.

The number of protons in a nucleus is equal to the number of electrons revolving around it. Therefore, an atom is neutral in normal state.

When one or more electrons are removed from an atom, it becomes a positively charged particle. When one or more electrons are added to an atom, it becomes negatively charged.

Q.2: Define insulator and conductor with some examples?

Ans:

• Insulator:
  Those materials which do not allow the charge to pass through them are called insulators. The electrons in an atom of an insulator are bound tightly with the nuclei and thus charge cannot pass through them.
  Examples: Wood, plastics, rubber, etc.

• Conductor:
  Those materials which allow the charges to pass through them are called conductors. In a conductor, some of the electrons are loosely bound and can move about freely within the material. These free electrons are responsible to conduct electricity in conductors.
  Examples: Copper, iron, aluminium, gold, silver, etc.

Q.3: What is Coulomb’s law? Derive the expression for it?

Ans:
Statement:
The force of attraction or repulsion between two charged particles is directly proportional to the product of their charges and inversely proportional to the square of the distance between the charges.

Mathematical Derivation:
If two charges $q_1$ and $q_2$ are placed at a distance $r$. According to the first part of Coulomb’s law, the force of attraction or repulsion is directly proportional to the product of their charges. Mathematically,

$$F \propto q_1 \cdot q_2 \tag{i}$$

And according to the second part of the law, the force of attraction or repulsion is inversely proportional to the square of the distance between them. Mathematically,

$$F \propto \frac{1}{r^2} \tag{ii}$$

Combining eqn. (i) and (ii), we get:

$$F = K \frac{q_1 \cdot q_2}{r^2}$$

Where $K$ is the constant of proportionality whose unit is $\text{Nm}^2/\text{C}^2$ and its value is $9 \times 10^9 \, \text{Nm}^2/\text{C}^2$. Value of this constant $k$ is commonly expressed in terms of another constant $\varepsilon_0$ (epsilon), as:

$$k = \frac{1}{4\pi \varepsilon_0}$$

Where $\varepsilon_0$ is called the permittivity of free space. So, Coulomb’s law can be written as:

$$F = \frac{1}{4\pi \varepsilon_0} \frac{q_1 \cdot q_2}{r^2}$$

Q.4: Define charge? Write down the SI unit of charge.

Ans:
Electric Charge:
Electric charge is a basic property of elementary particles of matter. The protons in an atom, for example, have a positive charge, the electrons have a negative charge, and the neutrons have zero charge. In an ordinary atom, the number of protons equals the number of electrons, so the atom normally has no net electric charge. An atom becomes negatively charged if it gains extra electrons, and it becomes positively charged if it loses electrons; atoms with net charge are called ions. Every charged particle is surrounded by an electric field, the area in which the charge exerts a force.

Unit of Charge:
The unit of charge in SI system is coulomb. One coulomb (1C) of charge being that quantity of charge which when placed one metre from an identical charge in vacuum repels it with a force of $8.99 \times 10^9$ newton (N).

The following are the submultiples of coulomb:

• 1 milli coulomb (1 mC) = $10^{-3}$ coulomb
• 1 micro coulomb ($\mu C$) = $10^{-6}$ coulomb
• 1 micro micro coulomb (f$\mu C$) = $10^{-12}$ coulomb

Q.5: What are the factors on which Coulomb’s force depends?

Ans:
There are three factors on which Coulomb’s force depends:

• Product of charges
• Distance between the charges
• Presence of dielectric

Q.6: What do you understand by electric field?

Ans:
Electric Field:
Electric field is defined as a region around a charge particle where another charge particle experiences an electric force when placed at any point in the field.

Q.7: What is electric field intensity? Write down its formula and unit?

Ans:
Electric Field Intensity:
Force per unit positive charge in an electric field is called electric field intensity. It is represented by $E$. It is a vector quantity.

Formula:
If $F$ is the force experienced by the charge $q$ when placed at a point in an electric field, then the electric field intensity $E$ at that point is given by:

$$\text{Electric Field Intensity} = \frac{\text{Force}}{\text{Charge}}$$ $$E = \frac{F}{q}$$ $$E = \frac{K \, q \, q_0}{r^2} \div q_0 = k \frac{q \, q_0}{r^2} \times \frac{1}{q_0}$$ $$E = k \frac{q}{r^2}$$ $$E = \frac{1}{4 \pi \varepsilon_0} \frac{q}{r^2}$$

Unit of electric field intensity:
The unit of electric intensity is newton per coulomb (N/C).

Q.8: On what factors electric field intensity depends?

Ans:
There are three factors on which electric intensity depends:

• Electric field intensity is directly proportional to the magnitude of the source charge.
• It is inversely proportional to the square of the distance from the charge to the field point.
• It is inversely proportional to the permittivity of the medium.

Q.9: Define electrostatic induction. Explain it with experiment?

Ans:
Electrostatic Induction:
When a charged body is brought near to an uncharged body, then the uncharged body gains some charge without any direct contact. This phenomenon is called electrostatic induction.

Experiment:

1. Two metal spheres A and B fitted with wooden stands are placed together so that they touch one another and thus form a single conductor.
2. A negatively charged ebonite rod is now brought near the sphere A such that it does not touch the sphere A. As a result, a positive charge is induced on sphere A and a negative charge on sphere B.
3. Still keeping the charged rod in the same position, the sphere B is moved away from the sphere A at a short distance.
4. The negatively charged rod is now removed, and then the sphere A and B are tested for charge.

To test the nature of charges on the spheres, an electroscope is used. It is observed that A is positively charged and B is negatively charged. Separation of charges by this phenomenon is known as electrostatic induction.

Q.10: What is a gold leaf electroscope? Explain its construction and working?

Ans:
Gold Leaf Electroscope:
It is a device that can be used for detecting charges.

Principle:
It works on the principle that like charges repel each other and unlike charges attract each other.

Construction: It consists of a glass case that contains two thin leaves of gold. The leaves are connected through a conductor to a metal ball or disk outside the case but are insulated from the case itself.

Working: If a charged object is brought close to the ball, a separation of charge is induced between the ball and the gold leaves. The two leaves become charged and repel each other. If the ball is charged by touching the charged object, the whole assembly of the ball and leaves acquires the same charge. In either case, the greater the amount of charge, the greater will be the divergence in the leaves. Whether a body is positively or negatively charged can be determined by bringing it near a charged electroscope.

Q.12: Define electric potential difference? What are its formula and unit?

Ans:
Electric Potential Difference: The work done in carrying a unit positive charge from one point to the other against the electric field intensity is called electric potential. The difference of electric potential level between two points is called electric potential difference.

Formula: Consider two points A and B at different potentials in an electric field. The potential difference between A and B is equal to the amount of work done by carrying a unit positive charge from A to B against the electric field, shown by $W_{AB}$.

$$\Delta V = V_A - V_B = \frac{W_{AB}}{q}$$ $$V = \frac{W}{q}$$

Unit: The SI unit of electric potential is joule per coulomb (J/C) or volt (V).

Definition of Volt: If one joule of work is done to move one coulomb charge from one point to another point, then the potential difference between the two points will be one volt.

Q.13: What is a capacitor? Explain the construction and working of a parallel plate capacitor?

Ans: Capacitor: A device that can store electric charge and electrical energy is called a capacitor.

Construction of a Parallel Plate Capacitor: It consists of two parallel conducting plates with air or some other insulator, called dielectric, between them.

Working: Two metallic plates A and B are fixed on an insulated stand. We charge the metallic plate A positively in small steps. This can be done by rubbing a glass rod against a silk cloth and then touching it with the plate. This process may be repeated many times to enhance the amount of charge on the plate, increasing its potential. After a while, the plate A cannot be charged anymore. The other plate will have a negative charge induced on it, and these positively and negatively charged plates hold each other. The stored electrical energy in a capacitor can be utilized according to the need.

Q.14: Define the capacity of a capacitor or capacitance? What are its formula and SI unit? Define farad?

Ans: Capacity of a Capacitor or Capacitance: It is the ability of a capacitor to store charge.

Formula: The charge $q$ on the plate of a capacitor is directly proportional to the electric potential difference $V$ between them.

$$q \propto V$$$$q = (\text{constant})V$$$$q = CV$$

Where $C$ is a constant whose value depends upon the area of the plates, the distance between the plates, and the medium between them. The constant $C$ is called the capacity of the capacitor.

$$C = \frac{q}{v}$$

Unit: The SI unit of capacity of a capacitor is Farad. It is denoted by F. Generally, capacitors are very small fractions of a Farad. Their capacities are usually specified in micro and pico farad.

1 μF (micro farad) = $10^{-6}$ farad
1 μμF (pico farad) = $10^{-12}$ farad

Definition of Farad: Farad (F) is defined as the capacity of that capacitor which stores a charge of 1 coulomb if the potential difference between the plates is 1 volt.

Q.15: What do you understand by electromotive force (e.m.f.)?

Ans: Electromotive Force (E.M.F.): The energy required to drive the charge around the circuit is called electromotive force. It is also defined as the potential energy applied to each unit of charge.

Formula:

$$\text{e.m.f.} = \frac{\text{Energy supplied}}{\text{Charge}}$$

Unit: The unit of e.m.f. is volt.

Q.16: What is the difference between potential difference (P.D.) and electromotive force (e.m.f.)?

Ans: The difference between P.D. and e.m.f. is that a source of e.m.f. in a circuit does work on the moving charges (supplies energy) whereas P.D. refers to the work done by the charges (expended energy) in passing through the resistance.

Q.17: Define an electric cell. What things do we need to make a cell? What are primary and secondary cells?

Ans: Electric Cell: A cell is a device which supplies electricity. An electric cell converts chemical energy into electrical energy.

Things We Need To Make A Cell: We need three things to make a cell: two electrodes and one container containing an electrolyte solution.

Primary Cell: Such type of cells whose working does not depend upon any external source is called primary cells. In these cells, the current is produced by the chemical actions between its components. When the chemicals are exhausted, they cannot produce any more current.

Examples: Voltaic cell, Daniell cell, Leclanche cell, and dry cell.

Secondary Cell: This type of cells can be recharged after they have run down by passing a current through them from an external source. This is known as the charging of a cell. As a result of charging, the cells regain chemical potential energy which is again used to produce current. This is why such cell is sometimes known as a storage cell or an accumulator.

Example: Lead-acid accumulator.

Q.18: Write down the construction and working of a voltaic cell?

Ans: Voltaic Cell: A device that produces an e.m.f. as a result of chemical reaction. This reaction occurs at the surface of two electrodes, each of which dips in an electrolyte.

Construction: It consists of two strips, one of zinc and the other of copper, in a glass vessel containing dilute sulphuric acid. The strips are called electrodes and sulphuric acid solution is known as an electrolyte. Both the strips are connected by copper wire. Zinc plate has a negative charge while the copper plate has a positive charge.

Working: When the zinc strip is placed in the acid solution, it reacts with the acid and begins to dissolve. Zinc atoms leave the strip and enter the solution. Each zinc atom that escapes from the strip leaves behind two electrons.

$$\text{Zn} \rightarrow \text{Zn}^{++} + 2e^{-}$$

Electrolyte which is $H_2SO_4$ changes into:

$$H_2SO_4 \rightarrow 2H^{+} + SO_4^{--}$$

These hydrogen ions take electrons from the copper plate. The copper plate becomes positively charged. The hydrogen molecules are formed and bubble off into the air.

$$2H^{+} + 2e^{-} \rightarrow H_2$$

When zinc plate and copper plate are joined with the help of a wire, a current will start to pass from the positive to the negative electrode of the cell, and the bulb is lighted if connected.

Q.19: Write down the construction and working of a Daniell cell?

Ans: Daniell Cell: It is a modified form of the simple cell. It is a primary cell having a negative pole of amalgamated zinc, standing in a porous pot containing dilute sulphuric acid.

Construction: It consists of a copper vessel containing saturated copper sulphate solution. The vessel itself behaves as the positive plate. The negative plate is an amalgamated zinc rod which stands in a porous pot filled with dilute sulphuric acid. The porous pot is placed at the center of the copper vessel. The two fluids are in contact with each other through the pores of the porous pot.

Q.20: Write down the construction and working of a Leclanche cell?

Ans: Leclanche Cell: It is an improved version of the Daniell cell and has an e.m.f. of about 1.5 V.

Construction And Working: It consists of a positive carbon electrode packed into a mixture of $MnO_2$ and powdered carbon in a porous pot. The porous pot stands in a glass jar filled with a solution of ammonium chloride. The negative zinc electrode is dipped in the solution of $NH_4Cl$.

The chemical reaction takes place between $NH_4Cl$, $MnO_2$, and Zn, resulting in the production of ammonia ($NH_3$), zinc chloride ($ZnCl_2$), water ($H_2O$), and manganese oxide ($Mn_2O_3$).

$$2MnO_2 + 2NH_4Cl + Zn \rightarrow Mn_2O_3 + H_2O + ZnCl_2 + 2NH_3$$

The essential electron exchange occurs when zinc metal (Zn) gives up electrons at the negative terminal to become zinc ions ($Zn^{++}$).

$$Zn \rightarrow Zn^{++} + 2e^{-}$$

Electrons flow through the external circuit to the carbon rod or positive terminal where they are taken up by the manganese.

Q.21: Write briefly about a dry cell?

Ans: Dry Cell: It is a modified form of the Leclanche cell. It is not perfectly dry but is called a dry cell because the ammonium chloride solution of the Leclanche cell is replaced by ammonium chloride paste.

Construction And Working: It consists of a container made of zinc, which serves as the negative terminal. It contains a paste of ammonium chloride, manganese dioxide, powdered carbon, a little water, and neutral filler as flour. A carbon rod in the center serves as the positive terminal. All the components are held together in a sealed plastic container, which prevents leakage and evaporation of moisture. It is dry and leak-proof; that is why these cells are widely used.

Q.22: Explain some defects of voltaic cells? How can these defects be prevented?

Ans: Polarization: In a voltaic cell, a large amount of hydrogen drifts towards the copper plate; only a part of these hydrogen ions reach the copper plate. This causes an accumulation of hydrogen around the copper plate, which prevents contact between the copper and the acid, and so stops the flow of current. Such a defect of voltaic cell is known as polarization.

Preventing From Polarization - Depolarization: The polarization may be prevented, to some extent, by giving the positive plate a rough surface from which the hydrogen bubbles break away more easily than from a smooth surface. The phenomenon of preventing hydrogen layer from being formed on the positive plate is known as depolarizing.

Local Action: Another defect of a voltaic cell is known as local action. It becomes prominent when the zinc plate has impurities such as carbon or iron. These impurities, together with zinc and acid, form tiny cells at the surface of the zinc plate. Due to chemical reactions in those tiny cells, zinc dissolves in the acid and bubbles of hydrogen are given off from the particles of impurities. This is known as local action and takes place even when the cell is not connected to the external circuit.

Preventing From Local Action: This defect can be removed by amalgamating the zinc plate. For this purpose, the zinc plate is dipped into sulphuric acid and then rubbed with mercury, which dissolves some of the zinc, forming a solution known as zinc amalgam which coats the plate.

Q.23: What is lead-acid accumulator? Explain its construction and working?

Ans: Lead-Acid Accumulator: It is a type of secondary cell and used to supply electric current.

Construction: It consists of a pair of lead plates A and B immersed in a vessel containing dilute sulphuric acid. In accumulators, several lead plates are held parallel to each other in the acid and then connected to the positive and negative electrodes of the cell.

Charging Of An Accumulator: Conversion of lead sulphate, present on the plates A and B, into lead oxide by the passage of direct current through the accumulator, is called charging of accumulator.

Discharging Of An Accumulator: The reverse process in which the current is driven out to an external circuit in the reverse direction is known as discharging of the accumulator.

Working: When the cell is working, the lead oxide-coated plate A becomes the positive terminal, and the metal plate B becomes the negative terminal. When these terminals are connected, current flows from A to B through the external circuit and from B to A through the acid. This action is called discharging. The following chemical reactions take place during discharging:

1. $PbO_2 + H_2 \rightarrow PbO + H_2O$
2. $PbO + H_2SO_4 \rightarrow PbSO_4 + H_2O$

The lead sulphate is insoluble in the electrolyte, and it forms a coating on the plate. At the negative plate:

$Pb^{++} + SO_4^{--} \rightarrow PbSO_4$

Continuation of Q.23:

When both the plates are coated with lead sulphate, the accumulator is completely discharged, and no current is drawn through it.

During the charging process, $H^+$ ions migrate to the negative plate B and convert the lead sulphate formed during discharge of the accumulator to metallic lead.

$$PbSO_4 + 2H_2O \rightarrow PbO_2 + 2H_2SO_4 + 2e^-$$

At the positive plate A,

$$PbSO_4 + 2H_2O \rightarrow PbO_4 + 2H_2SO_4 + 2e^-$$

The net result is the formation of a layer of lead peroxide on the plate A, a layer of spongy lead on the plate B, and an increase in the concentration of sulphuric acid. With the removal of $PbSO_4$ layers from the plates of the accumulator, it starts supplying current to the external circuit, and the accumulator is said to be charged again.

Q.24: What are the factors on which the capacity of a capacitor depends?

Ans: There are three factors on which the capacity of a capacitor depends:

• Surface area of the plates
• Distance between the two plates
• Nature of the dielectric used.

Q.25: Define electric current? What is its formula and unit?

Ans: Current: The flow of charge per unit time is called electric current.

Formula:

$$\text{Electric Current} = \frac{\text{Charge}}{\text{Time}}$$ $$I = \frac{q}{t}$$

Unit: In the SI system, the unit of current is ampere (A). It is denoted by A.

1 mA = $10^{-3}$ A
1 µA = $10^{-6}$ A

Definition of Ampere: If one coulomb of charge passes through a particular point in one second, then the current will be 1 ampere.

Q.26: Define resistance and its unit? What are the factors on which it depends?

Ans: Resistance: Resistance is an opposition to the motion of free electrons due to their collisions with each other.

Factors On Which Resistance Depends: The factors on which the resistance depends are as under:

• Nature of the conductor
• Length of the conductor
• Area of cross-section of the conductor
• Temperature of the conductor

Formula:

$$\text{Resistance} = \frac{\text{Potential difference}}{\text{Current}}$$ $$R = \frac{V}{I}$$

Unit: The unit of resistance is ohm (Ω) and is denoted by omega (Ω).

Definition Of Ohm (Ω): If one ampere current passes through a conductor when the potential difference across its ends is one volt, then the resistance of that conductor is one ohm.

1 MΩ = $10^6$ Ω
1 kΩ = $10^3$ Ω
1 mΩ = $10^{-3}$ Ω
1 µΩ = $10^{-6}$ Ω

Q.27: State Ohm’s law? Derive the equation V = IR?

Ans: Statement: According to Ohm’s law, "the current passing through a conductor is directly proportional to the potential difference, provided the temperature and other physical conditions of the conductor are kept constant."

Mathematical Derivation Of V = IR: Suppose the amount of current I is passing through a conductor, and the potential difference between the two ends of the conductor is V, then:

$$V \propto I$$ $$V = IR$$

Where R is a constant known as the resistance of the conductor. R is a physical property of the conductor.

Q.28: Define Electric circuit and Conventional current?

Ans: Electric Circuit: Any closed path through which an electric current can flow is called an electric circuit.

Conventional Current: Earlier scientists had no knowledge about electrons. They thought that current flows from positively charged body to negatively charged body. This current is known as conventional current, whereas the actual flow of current is the motion of electrons from negative terminal to positive terminal. The concept of conventional current is still in use.

Q.29: What do you understand by resistor? In how many ways resistors can be connected in a circuit?

Ans: Resistor: A thing or a device in an electric circuit that offers resistance in the way of current is called a resistor.

Resistors In A Circuit: Resistors are connected in an electric circuit in two ways:

• Series
• Parallel

Q.30: Draw diagrams of resistors in series and parallel circuits?

Ans: Resistors In Series Circuit:

(Diagram shows resistors $R_1, R_2, R_3$ connected in series with voltages $V_1, V_2, V_3$.)

Resistors In Parallel Circuit:

(Diagram shows resistors $R_1, R_2, R_3$ connected in parallel with branches $I_1, I_2, I_3$.)

Q.31: Write down the characteristics of a series circuit?

Ans: Characteristics Of A Series Circuit:

• Only one path is available for the flow of current. The same amount of current passes through each of the resistors.

  $I = I_1 = I_2 = I_3$

• The sum of potential differences across individual resistors is equal to the total voltage of the battery. If $V_1, V_2,$ and $V_3$ are the potential differences across the resistances $R_1, R_2,$ and $R_3$ respectively, then the voltage of the battery $V$ is given by:

  $V = V_1 + V_2 + V_3$

• The resistance $R_1, R_2,$ and $R_3$ can be replaced by a single resistance called equivalent resistance $R_e$. Equivalent resistance $R_e$ can be obtained by adding individual resistances combined in series:

  $R_e = R_1 + R_2 + R_3$

Q.32: Write down the characteristics of a parallel circuit?

Ans: Characteristics Of A Parallel Circuit:

• Many paths are available for the flow of current. The current passes through each resistor is different. The sum of all such current is equal to the total current supplied by the battery:

  $I = I_1 + I_2 + I_3$

• Potential difference across each resistor will be the same:

  $V = V_1 = V_2 = V_3$

• Hence, the resultant resistance of the circuit will be equal to the sum of the reciprocals of all the resistances in the circuit:

  $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$

Q.33: With the help of circuit diagram derive the expression $R_e = R_1 + R_2 + R_3 + \ldots$, when resistors are connected in series.

Ans: Consider three resistors $R_1, R_2,$ and $R_3$ are joined together in such a way that the same current $I$ passes through each of these resistors.

(Diagram shows resistors $R_1, R_2,$ and $R_3$ connected in series with voltages $V_1, V_2,$ and $V_3$.)

Continuing Derivation for Series Circuit:

$I = I_1 = I_2 = I_3$

These resistances are connected in series. Now by applying Ohm’s law for each resistor, we have:

• By using Ohm’s law for $R_1$: $V_1 = IR_1 \quad \text{(i)}$

• By using Ohm’s law for $R_2$: $V_2 = IR_2 \quad \text{(ii)}$

• By using Ohm’s law for $R_3$: $V_3 = IR_3 \quad \text{(iii)}$

For a series circuit, the sum of potential differences across individual resistors is equal to the total voltage of the battery. If $V_1, V_2,$ and $V_3$ are the potential differences across the resistors $R_1, R_2,$ and $R_3$ respectively, then the voltage of the battery $V$ is given by:

$V = V_1 + V_2 + V_3$

The resistances $R_1, R_2,$ and $R_3$ can be replaced by a single resistance $R_e$:

$IR_e = IR_1 + IR_2 + IR_3$

$IR_e = I(R_1 + R_2 + R_3)$

$R_e = R_1 + R_2 + R_3$

If there are more than three resistors, the above equation becomes:

$R_e = R_1 + R_2 + R_3 + \ldots$

Q.34: With the help of a circuit diagram, derive the expression $\frac{1}{R_e} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$, when resistors are connected in parallel?

Ans:

Consider resistances $R_1, R_2,$ and $R_3$ are connected in parallel between the two common points A and B. A battery of voltage $V$ is connected across A and B. The current $I$ provided by the battery is divided into $I_1, I_2$, and $I_3$ among the resistors $R_1, R_2,$ and $R_3$.

According to Ohm’s law, the current for each resistor will be:

(Diagram shows resistors $R_1, R_2,$ and $R_3$ connected in parallel with currents $I_1, I_2,$ and $I_3$ through each resistor.) 

I1​=R1​V​(i) $$I_2 = \frac{V}{R_2} \quad \text{(ii)}$$ $$I_3 = \frac{V}{R_3} \quad \text{(iii)}$$

Now, by adding equations (i), (ii), and (iii), we have:

$$I_1 + I_2 + I_3 = \frac{V}{R_1} + \frac{V}{R_2} + \frac{V}{R_3} \quad \text{(iv)}$$

But we know that:

$$I_1 + I_2 + I_3 = I$$ $$V = V_1 = V_2 = V_3$$

So, equation (iv) can be written as:

$$I = V \left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\right) \quad \text{(v)}$$

By Ohm’s law:

$$I = \frac{V}{R_e}$$ $$\frac{V}{R_e} = V \left(\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}\right)$$ $$\frac{1}{R_e} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}$$

If there are more than three resistors, the above equation becomes:

$$\frac{1}{R_e} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$$

Q.35: Define Direct current and Alternating current?

Ans:

Direct Current (D.C.): The current which does not change its direction is called direct current. It is denoted by D.C. It can be obtained by connecting the two ends of a conductor to the terminals of the battery.

Alternating Current (A.C.): The current which changes its direction many times in a second is called alternating current. It is denoted by A.C.

Q.36: State and explain Joule’s law? OR Derive the expression W=I²Rt?

Ans:

STATEMENT:

Joule’s law describes the rate at which resistance in a circuit converts electric energy into heat energy. The amount of heat per second that develops in a wire carrying a current is proportional to the electrical resistance of the wire and the square of the current. The heat evolved per second is equivalent to the electric power absorbed, or the power loss.

Derivation Of W=I²Rt:

Consider a charge q passing through a resistance R in time t when the potential difference V is maintained across its ends, then

$$W \propto q$$ $$W = qV \quad \text{(i)}$$

But by the definition of electric current, we know that

$$I = \frac{q}{t}$$ $$q = It$$

Putting the value q in eqn. (i), we have

$$W = ItV$$

From Ohm’s law, we know that V=IR, then the above equation becomes

$$W = It(IR)$$ $$W = I^2Rt$$

Q.37: Define power? Write its formula and units?

Ans:

POWER:

The rate of doing work is called power.

Formula:

$$\text{Power} = \frac{\text{Work done}}{\text{time}}$$ $$P = \frac{W}{t}$$

Unit:

The S.I. unit of power is watt.

Q.38: Find the relation between power, voltage and current?

Ans:

As we know that by the definition of power,

According To Joule’s Law:

$$P = \frac{W}{t} \quad \text{(i)}$$

According to Joule’s law:

$$W = I^2 Rt \quad \text{(ii)}$$

Put the value of $W$ from eqn. (ii) in eqn. (i), we get

$$P = \frac{I^2 Rt}{t}$$ $$P = I^2 R \quad \text{(iii)}$$

According to Ohm’s law, $V = IR$, then eqn. (iii) becomes

$$P = I(IR)$$ $$\boxed{P = IV}$$

Q.39: What is the commercial unit of electrical energy?

Ans:

The unit of power is watt and the unit of time is second hence the unit of energy is watt-second. But this is a small unit and for normal use, the time is most taken in hours so that the unit of electrical energy is taken as kilowatt-hours (kWh). Thus:

$$\text{Energy in kWh} = P \times t \times 1000$$

Where $P$ is expressed in watts and in hours. The kilowatt-hour is the commercial unit in which the electrical energy is supplied.

Q.40: What are the factors on which dissipation of heat depends?

Ans:

The factors on which dissipation of heat depends are as follows:

• It is directly proportional to the amount of current.
• It is directly proportional to the time of flow of current.
• It is directly proportional to the potential difference applied.

Q.41: Explain the circuits in our houses?

Ans:

Electricity usually comes to our homes by two wires or lines, the live (L) wire and the neutral (N). The potential difference between these wires is 220V. The neutral wire is connected to the earth about every 100m.

Circuits In Parallel:

Every circuit in our homes is connected in parallel with the main supply i.e., across the live wire and neutral wire and receives the full mains potential difference of 220V.

Connection Of Switches And Fuses:

These are always in the live wire side of the circuit.

Staircase Circuit:

The lamp is controlled from two places by two-way switches.

Ring Main Circuit:

The live and neutral wires are thick and each run in a complete ring around the house; and the power sockets, each rated at 13A, are tapped off from them. Thinner wires can be used for each socket since the current to each socket is less than 13A. The ring has a 30A fuse, and if it has ten sockets, all can be used so long as the total current does not exceed 30A.

Fused Plug:

Only one type of plug is used in a ring main circuit. It has its own cartridge fuse.

Earthing And Safety:

A ring main circuit has a third wire connected to a metal pipe in the house or to an earth connection of the main supply. This third wire is a safety precaution to prevent electric shock.

Q.42: Why do we always put switches and fuses in the live wire side of the circuit?

Ans:

If they were in the neutral side, then the lamp and power sockets would be ‘live’ even when switches were off or fuses blown. A fatal shock could then be obtained by the person who touches the element of an electric wire when it was switched off. That is why we always put switches and fuses in the live wire of the circuit.

Q.43: Define fuse?

Ans:

A fuse is a safety device. It consists of a piece of metal wire of low melting point. When current exceeds the safety limits, the heat melts the wire, thus breaking the passage of current.

Q.44: Differentiate between insulator and conductor?

Insulator	Conductor
They do not allow electric current to pass through it.	They allow electric current to pass through it.
Electrons in their atoms are bound tightly by the nucleus.	Electrons in their atoms are loosely bound with the nuclei.
No free electrons are present.	A lot of free electrons are present.
Examples: Wood, plastic, rubber, etc.	Examples: Copper, gold, silver, iron, etc.

Q.45: Differentiate between current and potential difference?

Current	Potential Difference
Flow of charge from negative to positive.	Change in potential energy per unit charge between two points.

Q.46: Differentiate between series circuit and parallel circuit?

Series Circuit	Parallel Circuit
Current flows in a single path.	Current flows in multiple paths.
Same current flows through each component. $I = I_1 = I_2 = I_3 = \ldots$	Different currents flow in each component. $I = I_1 + I_2 + I_3 + \ldots$
Potential difference in each component is different. $V = V_1 + V_2 + V_3 + \ldots$	Same potential difference is present in each component. $V = V_1 = V_2 = V_3 = \ldots$
Net resistance of all the resistances is equal to the sum of individual resistance. $R = R_1 + R_2 + R_3 + \ldots$	Net resistance of all the resistances is equal to the sum of the reciprocal of individual resistances. $\frac{1}{R} = \frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3} + \ldots$

Q.47: Differentiate between alternating current and direct current?

Alternating Current	Direct Current
The direction of current changes many times in a second.	The direction of current does not change.
It is produced by generators.	It is produced by cells.
It has frequency.	It has no frequency.
It is not dangerous.	It is too dangerous.