# Current Electricity Class 12 Problems with Solutions:Important Questions for Exams

JEE Mains & AdvancedGet Current Electricity important problems with solutions for class 12 Boards exams. View the Physics Question Bank Class 12 for other chapters problems and solutions along with Current Electricity. These important questions will play significant role in clearing concepts of Physics. This question bank is designed keeping NCERT in mind and the questions are updated with respect to upcoming Board exams. You will get here all the important solved questions for class 11 & 12 Physics chapters. Learn all the concepts of Current Electricity chapter with these problems and solutions and prepare well for class 12 and other exams. **Click Here for Detailed Chapter-wise Notes of PHYSICS for Class 12th, JEE & NEET.**

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**Q. What happens to the drift velocity $v_{\mathrm{d}}$ of electron and to the resistance $R,$ if length of the conductor is doubled (keeping potential difference unchanged) $?$**

*l*is doubled, drift velocity becomes half of the initial value. (ii) When

*l*is doubled, resistance becomes twice the initial value.

**Q. A low voltage supply from which one needs high currents must have very low internal resistance. Why ?**[NCERT]

**Q. Is there a net field inside the cell when the circuit is closed and a steady current passes**

**through? Explain.**[NCERT]

**Q. A high tension (HT) supply of say, $6 k V$ must have**

**a very large internal resistance. Why?**[NCERT]

**Q. In a potentiometer arrangement, a cell of**[NCERT]

*emf*1.25*V*gives a balance point at 35.0 cm length of the wire. If the cell is replaced by another cell and the balance point shifts to 63.0 cm, what is the*emf*of the second cell ?**Q.**A galvanometer coil has a resistance of and the metre shows full scale deflection for a current of 4

*mA*. How will convert the metre into an ammeter of range 0–6

*A*. [NCERT]

**Q. A galvanometer coil has a resistance of and the metre shows full scale deflection for a current of 3**[NCERT]

*mA*. How will you convert the metre into an voltmeter of range 0 to 18*V*?**Q.**The electrons drift speed is estimated to be only a few

*$m m s^{-1}$*for currents in range of a few ampere. How then is current established almost the instant a circuit is closed ?

**[NCERT]**

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**Q. When electrons drift in a metal from lower to higher potential, does it mean that all**

**the ‘free’ electrons of the metal are moving in the same direction ?**[NCERT]

**Q. Currents of the order of 0.1**

*A*, through the human body are fatal. What causes the**Death :heating of the body due to electric current or some thing else ?**[NCERT]

**Q. Choose correct alternative**(a) Alloys of metals usually have (greater/less) resistivity than that of their constituent metals (b) Alloys usually have much (lower/higher) temperature coefficients of resistance than pure metals. (c) The resistivity of the alloy manganin is nearly independent of/increases rapidly with increase of temperature. (d) The resistivity of a typical insulator (e.g. amber) is greater than that of a metal by a factor of the order of $\left(10^{22} / 10^{3}\right)$ [NCERT]

**Q. A silver wire has a resistance of $2.1 \Omega$ at $27.5^{\circ} \mathrm{C},$ and a resistance of $2.7 \Omega$ at $100^{\circ} \mathrm{C}$. Determine the temperature coefficient of resistivity of silver?**[NCERT]

**Q. A heating element using nichrome connected to a 230**[NCERT]

*V*supply draws an initial current of 3.2*A*which settles after a few seconds to a steady value of 2.8*A*. What is the steady temperature of the heating element if the room temperature is $27.0^{\circ} \mathrm{C}$? Temperature coefficient of resistance of nichrome averaged over the temperature range involved is $1.70 \times 10^{-4} \circ C^{-1}$*i.e.*heat produced is equal to heat lost to the surrounding. Temperature will not rise further.

**Q. The number density of conduction electrons in a copper conductor estimated is $8.5 \times 10^{28} \mathrm{m}^{-3}$. How long does an electron take to drift from one end of a wire 3.0**[NCERT]

*m*long to its to its other end ? The area of cross-section of the wire is $2.0 \times 10^{-6} \mathrm{m}^{2}$ and it is carrying a current of 3.0*A*.**Here, $n=8.5 \times 10^{28} \mathrm{m}^{-3} ; \quad l=3.0 \mathrm{m} ; \quad A=2.0 \times 10^{-6} \mathrm{m}^{2}$**

**$I=3.0 \mathrm{A}, t=?$**

**Q. A cell of**[NCERT]

*emf*1.5*V*and internal resistance is connected to a (non-linear) conductor whose*V–I*graph is shown in figure. Obtain graphically the current drawn from the cell and its terminal voltage.*V*and

*I*satisfying above equation are

*V*(volt)

*I*(ampere) Graph of these values is a line represented by dotted lines. There is a common point between the dotted line and the graph given. This corresponds to 1volt and 1

*A*. So, the cell given supplies 1

*A*current for 1volt.

**Q. A battery of**[NCERT]

*emf*9*V*and negligible internal resistance is connected to a $3 k \Omega$ resistor. The potential drop heross a part of the resistor (between point $A$ and $B$ in figure) is measured by (i) a $20 \mathrm{k} \Omega$ voltmeter. (ii) a $1 \mathrm{k\Omega}$ voltmeter. and (iii) both the voltmeters are connected across $A B .$ In which case would you get the (i) highest, (ii) lowest reading?*AB*decrease by a minimum amount), will give the highest reading.

**In case $(a), R_{V}=20 k \Omega$**

**In case $(b), R_{V}=1 k \Omega$**

**In case $(c), \frac{1}{R_{V}}=\frac{1}{20}+\frac{1}{1}=\frac{1+20}{20}$ or $R_{V}=\frac{20}{21} k \Omega$**

**(i) Since in case $(a)$, the resistance of voltmeter is maximum ( $20 k \Omega$ ) ; it will draw minimum current and hence it will give the maximum reading.**

**(ii) Since in case $(c), R_{\mathrm{v}}$ is minimum $\left(\frac{20}{21} k \Omega\right),$ it will**give lowest reading.

**Q. Storage battery of a car has an emfof 12 V. If the internal resistance of the battery is $0.4 \Omega,$ what is the maximum current that can be drawn from the battery ?**[NCERT]

*i.e.*

**Q. Six lead-acid type of secondary cells each of**[NCERT]

*emf*2.0*V*and internal resistance $0.015 \Omega$ are joined in series to provide a supply to a resistance of $8.5 \Omega$ What are the current drawn from the supply and its terminal voltage ?**Ans. Total emf of the combination $=6 \times 2 V=12$ volt**

**Total internal resistance $=6 \times 0.015 \Omega=0.09 \Omega$**

**External resistance of the circuit $=8.5 \Omega$**

**Total resistance of the circuit $=8.5+0.09=8.59 \Omega$**

**Current drawn, $I=\frac{12}{8.59}=1.4 A$**

**Terminal potential difference, $\mathrm{V}=12-1.4 \times 0.09$**

**$=12-0.126=11.9$ volt**

**Q. A secondary cell after long the use has an**

*emf*of 1.9*V*and a large internal resistance $380 \Omega$ of What maximum current can be drawn from the cell ? Could the cell drive the starting motor of a car ?**Ans. Maximum current $=\frac{1.9}{380}=0.005 A,$ A large current**is required by a motor starter for a few second. So it cannot be used in a car.

**Q. Two identical cells of**[NCERT]

*emf*1.5*V*each joined in parallel provide supply to an external circuit consisting of two resistors of each joined in parallel. A very high resistance voltmeter reads the terminal voltage of the cells to be 1.4*V*. What is the internal resistance of each cell?*emf*is equal to the

*emf*of either cell.

*i.e.*volt If $^{c} r^{,}$ is internal resistance of each cell, then $\frac{1}{r_{P}}=\frac{2}{r}$ P $r_{P}=0.5 r$

**External resistance is $R_{P}=\frac{17}{2} \Omega=8.5 \Omega$**

**Terminal potential difference $V=1.4$ volt**

**$r_{P}=\frac{E-V}{V} R_{P}$. $\mathrm{B}$. $5 r-\frac{1.5-1.4}{1.4} \times 8.5$**

**$\mathrm{B} \quad r=\frac{17}{14} \Omega=1.2 \Omega$**

**Q. (a) A d.c. supply of 120**

*V*is connected to a large resistance*X*. A voltmeter of resistance 10

*k*W placed in series in the circuit reads 4*V*. What is the value of*X*?**(b) What do you think is the purpose in using a voltmeter, instead of an ammeter, to determine the large resistance**[NCERT]

*X*?**Q. A galvanometer with a coil of resistance $12.0 \Omega$ shows a full scale deflection for a current of 2.5**[NCERT]

*mA*. How will you convert the galvanometer into (a) an ammeter of range 0 to 7.5*A*, (b) a voltmeter of range 0 to 10.0*V*? Determine the net resistance of the metre in each case. When an ammeter is put in a circuit, does it read (slightly) less or more than the actual current in the original circuit ? When a voltmeter is put across a part of the circuit, does it read (slightly) less or more than the original voltage drop ? Explain.*R*be the resistance in series with galvanometer. As $\quad R=\frac{V}{I_{g}}-G$ $\backslash R=\frac{10}{2.5 \times 10^{-3}}-12=4000-12=3988 \Omega$ $\therefore \quad$ Net $\quad$ resistance of $\quad$ the voltmeter $=3988+12=4000 \Omega$ A voltmeter is used in parallel with the circuit. It will also allow some current to pass through it. Due to it, the current in the circuit across the two points where voltmeter is connected decreases and hence potential difference decreases. Therefore, the voltmeter reads slightly less value.

**Q. A voltmeter reads 5.0**[NCERT]

*V*at full scale deflection and is graded according to its resistance per volt at full scale deflection as $5000 \Omega / V$ How will you convert it into a voltmeter that reads 20*V*at full scale deflection ? Will it still be graded as $5000 \Omega / V$? Will you prefer this voltmeter to one that is graded as $2000 \Omega / V ?$?**Q. You are given two resistors**[NCERT]

*X*and*Y*whose resistances are to be determined using an ammeter of resistance $0.5 \Omega$ and a voltmeter of resistance $20 \times 10^{3} \Omega$ It is known that*X*is in the range of a few ohms, while*Y*is in the range of several thousand ohms. In each case, which of the following two connections would you choose for the measurement of resistance ?*X*is small; (ii) Circuit should be used to measure it.

**As $\quad$ Resistance $(X)=\frac{\text { Reading of } V}{\text { Reading of } A}$**In circuit (i) it will affect the reading of ammeter. For resistance

*X*is very large, (i) circuit should be used to measure it. As resistance

*Y*is very large in comparison to the resistance of ammeter, it does not affect the reading of ammeter.

**Q. The earth’s surface has a negative surface charge density of $10^{-9} \mathrm{Cm}^{ 2}$ . The potential difference of 400**[NCERT]

*kV*between the top of the atmosphere and the surface results (due to low conductivity of the lower atmosphere) in current of only 1800*A*over the entire globe. If there were no mechanism of sustaining atmospheric electric field; how much time (roughly) would be required to neutralise (because there is a mechanism to replenish electric charges namely the continual thunder storms and lightning in different parts of the globe) Radius of the earth$=6.37 \times 10^{6} \mathrm{m}$**Q. (a) Estimate the average drift speed of conduction electrons in a copper wire of cross sectional area $1.0 \times 10^{-7} \mathrm{m}^{2}$ carrying a current of 1.5**[NCERT]

*A.*Assume that each copper atom constributes roughly one conduction electron. The density of copper is $9.0 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3}$and its atomic mass is $63.5 u$ (b) Compare the drift speed of obtained above with, (i) Thermal speeds of copper atoms at ordinary temperatures. (ii) Speed of propagation of electric field along the conductor which causes the drift motion.*i.e.*, electrons drift in the direction of increasing potential. The drift speed $v_{d}$ is given by equation $v_{d}=\frac{1}{n e A}$ Now, $e=1.6 \times 10^{-19} \mathrm{C}, A=1.0 \times 10^{-7} \mathrm{m}^{2}, \mathrm{I}=1.5 \mathrm{A}$. The density of conduction electrons, $n$ is equal to the number of atoms per cubic metre (assuming one conduction electron per $C u$ atom as is responsible from its valence electron count of one). Acubic metre of copper has mass of $9.0 \times 10^{3} \mathrm{kg}$. Since $6.0 \times 10^{23}$ copper atoms have a mass of $63.5 \mathrm{g} .$ (b) (i) At a temperature $T$, the thermal speed of a copper atom of mass $M$ is obtained from [ $\left.<(1 / 2) M v^{2}>=(3 / 2) k_{B} T\right]$ and is thus typically of the order of $\sqrt{k_{B} T / M},$ where $k_{B}$ is the Boltzmann constant. For copper at $300 K,$ this is about $2 \times 10^{2} m / s .$ This figure indicates the random vibrational speeds of electrons is much smaller, about $10^{-5}$ times the typical thermal speed at ordinary temperatures. (ii) An electric field travelling along the conductor has a speed of an electromagnetic wave, namely equal to $3.0 \times 10^{8} \mathrm{ms}^{-1}$. The drift speed is in comparison, extremely small, smaller by a factor of $10^{-11}$.

**Q. 4 cells of identical**

*emf**E*, internal resistance*r*, are connected in series to a variable resistor. The following graph shows the variation of terminal voltage of the combination with the current output*r*

**Q. Determine the current in each branch of the network shown in figure**

*ADCA*gives.

**$10-4\left(I_{1}-I_{2}\right)+2\left(I_{2}+I_{3}-I_{1}\right)-I_{1}=0$**…(i)

**that is, $7 I_{1}-6 I_{2}-2 I_{3}=10$**

**For the closed loop $A B C A,$ we get**

**$10-4 I_{2}-2\left(I_{2}+I_{3}\right)-I_{1}=0$**

**that is, $I_{1}+6 I_{2}+2 I_{3}=10$**…(ii) For the closed loop $B C D E B,$ we get $5-2\left(I_{2}+I_{3}\right)-2\left(I_{2}+I_{3}-I\right)=0$ that is, $21_{1}-4 I_{2}-4 I_{3}=-5$ …(iii) Equations (i), (ii) and (iii) are three simultaneous equations in three unknowns. These can be solved by the usual method to give $I_{1}=2.5 A, \quad I_{2}=\frac{5}{8} A, \quad I_{3}=1 \frac{7}{8} A$ The currents in the various branches of the network are $A B: \frac{5}{8} A, C A: 2 \frac{1}{2} A, D E B: 1 \frac{7}{8} A$ $A D: 1 \frac{7}{8} A, C D: 0 A, B C: 2 \frac{1}{2} A$ It is easily verified that Kirchhoff’s second rule applied to the remaining closed loops does not provide any additional independent equation, that is, the above values of currents satisfy the second rule for every closed loop of the network. For example, the total voltage drop over the closed loop

*BADEB*$5 \mathrm{V}+\left(\frac{5}{8} \times 4\right) \mathrm{V}-\left(\frac{15}{8} \times 4\right) \mathrm{V}$ equal to zero, as required by Kirchhoff's second rule

**Q. Figure shows a 2.0**[NCERT]

*V*potentiometer used for the determination of internal resistance of a 1.5*V*cell. The balance point of the cell in open circuit is 76.3 cm. When a resistor of $9.5 \Omega$ is used in the external circuit of the cell, the balance point shifts to 64.8 cm length of the potentiometer wire. determine the internal resistance of the cell.**Q. Figure shows a potentiometer circuit for comparison of two resistances. The balance point with a standard resistor $R=10.0 \Omega$ is found to be 58.3 cm, while that with the unknown resistance**[NCERT]

*X*is 68.5 cm. Determine the value of*X*. What might you do if you failed to find a balance point with the given cell of*emf E*?*emf E*, if the potential drop across

*R*or

*X*is greater than the potential difference across the wire

*AB*. In order to obtain the balance point with the given cell

*E*, either the

*emf*of the auxiliary battery (battery connected between the terminals

*A*and

*B*) should be increased or a suitable resistance should be put in series with

*R*and

*X*(so as to decrease the potential drop across the wire

*AB*).

**Q. The four arms of a Wheatstone bridge have the following resistance**: [NCERT]

**$A B=100 \Omega, B C=10 \Omega, C D=5 \Omega,$ and $D A=60 \Omega$**

**A galvanometer of 15W resistance is connected across**

*BD.*Calculate the current through the galvanometer when a potential difference of 10*V*is maintained across*AC.**BADB*, we have $100 I_{1}+15 I_{g}-60 I_{2}=0 \quad \mathrm{P} 20 I_{1}+3 I_{g}-12 I_{2}=0 \quad \ldots(1)$ Considering the mesh

*BCDB,*we have $10\left(I_{1}-I_{S}\right)-15 I_{S}-5\left(I_{2}+I_{S}\right)=0$ $10 I_{1}-30 I_{S}-5 I_{2}=0 \mathrm{P} 2 I_{1}-6 I_{g}-I_{2}=0$ …(ii) Considering the mesh $A D C E A$ 60 $I_{2}+5\left(I_{2}+I_{g}\right)=10$ B $65 I_{2}+5 I_{g}=10 \mathrm{P} 13 I_{2}+I_{g}=2$ …(iii) $\begin{array}{ll}{\text { Multiplying equation (ii) by } 10} \\ {20 I_{1}-60 l_{s}-10 I_{2}=0} & {\ldots \ldots(\mathrm{iv})}\end{array}$ From equations (iv) and (i) we have $63 I_{g}-2 I_{2}=0$ $I_{2}=31.5 I_{g}$ …(v) Substituting the value of into equation (iii), we get $13\left(31.5 I_{g}\right)+I_{g}=2 \mathrm{P} I_{g}=4.87 \mathrm{mA}$

**Q. A resistance of**[NCERT]

*R*W draw current from a potentiometer. The potentiometer has a total resistance $R_{0}$ W (figure). A voltage*V*is supplied to the potentiometer. Derive an expression for the voltage across*R*when the sliding contact is in the middle of the potentiometer.*A*and

*B*. Hence, the total resistance between

*A*and

*B*, say

*$R_{1}$*, will be given by the following expression :

**Q. A network of resistors is connected to a 16**[NCERT]

*V*battery with internal resistance of 1W, as shown in figure (a) Compute the equivalent resistance of the network. (b) Obtain the current in each resistor (c) Obtain the voltage drops $V_{A B}, V_{B C}$ and $V_{C D}$*R*of the network is obtained by combining these resistors (2W and 4W) with 1W in series, that is $R=2 \Omega+4 \Omega+1 \Omega=7 \Omega$ (b) The total current

*I*in the circuit is $I=\frac{E}{R+r}=\frac{16 \mathrm{V}}{(7+1) \Omega}=2 \mathrm{A}$ Consider the resistors between A and B. If $I_{1}$ is the current in one of the 4 W resistors and $I_{2}$ the current in the other. $I_{1} \times 4=I_{2} \times 4$ that is, $I_{1}=I_{2},$ which is otherwise obvious from the symmetry of the two arms. But $I_{1}+I_{2}=I=2 A .$ Thus, $I_{1}=I_{2}=1 A$ that is, current in each $4 \mathrm{W}$ resistor is $1 \mathrm{A}$. Current in $1 \mathrm{W}$ resistor between $\mathrm{B}$ and $\mathrm{C}$ would be $2 \mathrm{A}$. Now, consider the resistance between $\mathrm{Cand} \mathrm{D} .$ If $I_{3}$ is the current in the $12 \mathrm{W}$ resistor, and $I_{4}$ in the $6 \mathrm{W}$ resistor. $I_{3} \times 12=I_{4} \times 6,$ i.e., $I_{4}=2 I_{3}$ But, $I_{3}+I_{4}=I=2 A$ Thus, $I_{3}=\left(\frac{2}{3}\right) A, I_{4}=\left(\frac{4}{3}\right) A$ that is, the current in the $12 \mathrm{W}$ resistor is $(2 / 3) \mathrm{A},$ while the current in the 6 Wresistor is $(4 / 3) \mathrm{A}$. (c) The voltage drop across $A B$ is $V_{A B}=I_{1} \times 4=1 A \times 4 \Omega=4 \mathrm{V}$. This can also be obtained by multiplying the total current between

*A*and

*B*by the equivalent resistance between

*A*and

*B*, that is $V_{A B}=2 A \times 2 \Omega=4 V$ The voltage drop across $B C$ is $V_{B C}=2 A \times 1 \Omega=2 V$ Finally, the voltage drop across $C D$ is $V_{C D}=12 \Omega \times I_{3}=12 \Omega \times\left(\frac{2}{3}\right) A=8 \mathrm{V}$ This can alternately be obtained by multiplying total current between

*C*and

*D*by the equivalent resistance between

*C*and

*D*, that is $V_{C D}=2 A \times 4 \Omega=8 \mathrm{V}$ Note that the total voltage drop across

*AD*is 4

*V*+ 2

*V*+8

*V*= 14

*V*. Thus, the terminal voltage of the battery is 14

*V*, while its emf is 16

*V*. The loss of the voltage (=2

*V*) is accounted for by the internal resistance 1W of the battery $[2 A \times 1 \Omega=2 \mathrm{V}]$.

**Q. A battery of 10**[NCERT]

*V*and negligible internal resistance is connected across the diagonally opposite corners of a cubical network consisting of 12 resistors each of resistance 1 W. Determine the equivalent resistance of the network and the current along each edge of the cube.*AA’*,

*AD*and

*AB*are obviously symmetrically placed in the network. Thus, the current in each must be the same say,

*I*. Further, at the corners

*A’*,

*B*and

*D*, the incoming current

*I*must split equally into the two outgoing branches. In this manner, the current in all the 12 edges of the cube are easily written down in terms of

*I*, using Kirchhoff’s first rule and the symmetry in the problem. Next take a closed loop, say,

*ABCC’EA*, and apply Kirchhoff’s second rule. $-I R-(1 / 2) I R-I R+E=0$ Where

*R*is the resistance of each edge and

*E*the

*emf*of battery. Thus, $E=\frac{5}{2} I R$ The equivalent resistance $R_{\mathrm{eq}}$ of the network is For $R=1 \Omega R_{e q}=(56 / \Omega \text { and for } E=10 \mathrm{V},$ the total current $(=3 \mathrm{I})$ in the network is $3 I=10 \mathrm{V} / 156 \mathrm{R}=12 \mathrm{A},$ i.e. $I=4 \mathrm{A}$ The current flowing in each edge can now be read off from the figure \

**Q. Figure shows a potentiometer with a cell of 2.0**

*V*and internal resistance $0.40 \Omega$ maintaining a potential drop across the resistor wire*AB*. A standard cell which maintains a constant*emf*of 1.02*V*(for very moderate currents upto a few m*A*) gives a balance point at 67.3 cm length of the wire. To ensure very low currents drawn from the standard cell, a very high resistance of $600 \mathrm{k\Omega}$ is put in series with it, which is shorted close to the balance point. The standard cell is then replaced by a cell of unknown*emf**E*and the balance point found similarly, turns out to be at 82.3 cm length of the wire.**(i) What is the value**

*E*?**(ii) What purpose does the high resistance of $600 \mathrm{k\Omega}$ have?**

**(iii) Is the balance point affects by this high resistance ?**

**(iv) Is the balance point affected by the internal resistance of the driver cell ?**

**(v) Would the method work in the above situation if the driver cell of the potentiometer had an**

*emf*of 1.0*V*instead of 2.0*V*?**(vi) Would the circuit work well for determining an extremely small em.f. say of the order of a few m**[NCERT]

*V*(such as the typical*emf*of a thermo-couple) ? If not, how will you modify the circuit ?*E*is greater than

*emf*of the driver cell of the potentiometer, there will be no balance point on the wire

*AB*. (vi) Circuit would not be suitable, because the balance point (for

*E*of the order of a few

*mV*) will be very close to the end

*A*and the percentage error in measurement will be very large. The circuit is modified by putting a suitable resistor

*R*in series with the wire

*AB*so that potential drop across

*AB*is only slightly greater than the

*emf*to be measured. Then the balance point will be at larger length of the wire and the percentage error will be much smaller.

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