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Current Electricity-02-Objective Sol.

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OBJECTIVE LEVEL - I 1. A conductor of area of cross-section A having charge carriers, each having a charge q is subjected to a potential V. The number density of charge carriers in the conductor is n and the charge carriers along with their random motion are moving with average velocity v. A current I flows in the conductor. If j is the current density, then → (a) j nqV , in the direction of charge flow → (b) j nqv , in the direction opposite to charge flow (c) | j | nqV , in the direction perpendicular to charge flow (d) | j | nqv , in the direction of charge flow. 2. Two electric bulbs A and B are designed for the same voltage. Their power rating are PA and PB respectively, with PA>PB. If they are joined in series across a V-volt supply, (a) A will draw more power than B (b) B will draw more power then A (c) the ratio of powers drawn by them will depend on V (d) A and B will draw the same power. 3. A non-conducting ring of radius R has two positive point charges lying diametrically opposite to each other, each of magnitude Q. The ring rotates with an angular velocity . If I is the equivalent current then, (a) I Q (b) I 2Q (c) I Q (d) I = ZERO. 4. Three copper wires have their lengths in the ratio 5 : 3 : 1 and their masses are in the ratio 1 : 3 : 5. Their electrical resistance will be in the ratio (a) 5 : 3 : 1 (b) 1 : 3 : 5 (c) 125 : 15 : 1 (d) 1 : 15 : 125. 5. Sixteen resistors each of resistance 16 are connected in the cir- cuit as shown. The net resistance between AB is (a) 1 (b) 2 (c) 3 (d) 4 . A B 6. Two nonideal batteries are connected in parallel. Consider the following statemnents: (A) The equivalent emf is smaller than either of the two emfs (B) The equivalent internal resistance is smaller than either of the two internal resistances (a) Both A and B are correct (b) A is correct but B is worng (c) B is correct but A is worng (d) Both A and B are worng. 7. The equivalent resistance between points A and B in the circuit A B shown is 2R R R (a) R (b) 2 R R (c) 4 (d) 8 . 8. In the circuit shown E, F, G and H are cells of e.m.f. 2V, 1V, 3V and 1V respectively and their internal resistance are 2 , 1 . 3 D B and 1 respectively. (a) V V 2 V (b) V V 2 V D B 13 D B 13 (c) V 13 V G 21 = Potential difference across G (d) V 19 V Potential difference across H. H 13 9. The e.m.f. and the internal resistance of a source which is equivalent to two batteries which are connected in parallel having e.m.f.’s E and r. E1 and E2 and internal resistances r1 and r2 respectively are E E1r1 E2 r2 ; r r r E E1r2 E2 r1 ; r r r (a) (c) (r1 r2 ) E E1r2 E2 r1 ; r 1 2 r1r2 (b) (d) (r1 r2 ) E E1r1 E2 r2 ; r 1 2 r1r2 . (r1 r2 ) r1 r2 (r1 r2 ) r1 r2 10. In the circuit shows in figure, the steady state voltage drop across R3 the capacitor is VC . V C V VR1 V VR 2 R (

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- OBJECTIVE LEVEL - I 1. A conductor of area of cross-section A having charge carriers, each having a charge q is subjected to a potential V. The number density of charge carriers in the conductor is n and the charge carriers along with their random motion are moving with average velocity v.Acurrent I flows in the conductor. If j is the current density, then (a) j nqV , in the direction of charge flow (b) j nqv , in the direction opposite to charge flow (c) | j| nqV , in the direction perpendicular to charge flow (d) | j| nqv , in the direction of charge flow. . 2. Two electric bulbs A and B are designed for the same voltage. Their power rating are PA and PB respectively, with PA >PB . If they are joined in series across a V-volt supply, (a) A will draw more power than B (b) B will draw more power then A (c) the ratio of powers drawn by them will depend on V (d) A and B will draw the same power. 3. A non-conducting ring of radius R has two positive point charges lying diametrically opposite to each other, each of magnitude Q. The ring rotates with an angular velocity . If I is the equivalent current then, (a) I Q (b) 2Q I (c) Q I (d) I = ZERO. 4. Three copper wires have their lengths in the ratio 5 : 3 : 1 and their masses are in the ratio 1 : 3 : 5. Their electrical resistance will be in the ratio (a) 5 : 3 : 1 (b) 1 : 3 : 5 (c) 125 : 15 : 1 (d) 1 : 15 : 125. A B 5. Sixteen resistors each of resistance 16 are connected in the cir- cuit as shown. The net resistance between AB is (a) 1 (b) 2 (c) 3 (d) 4 . 6. Two nonideal batteries are connected in parallel. Consider the following statemnents: (A) The equivalent emf is smaller than either of the two emfs (B) The equivalent internal resistance is smaller than either of the two internal resistances (a) Both A and B are correct (b) A is correct but B is worng (c) B is correct but A is worng (d) Both A and B are worng.
- A B 2R R 2R 7. The equivalent resistance between points A and B in the circuit shown is (a) R (b) R 2 (c) R 4 (d) R 8 . D A F E B G C H 2 8. In the circuit shown E, F, G and H are cells of e.m.f. 2V, 1V, 3V and 1V respectively and their internal resistance are 2 , 1 . 3 and 1 respectively. . (a) D B 2 V V V 13 (b) D B 2 V V V 13 (c) G 13 V V 21 = Potential difference across G (d) H 19 V V 13 Potential difference across H. 9. The e.m.f. and the internal resistance of a source which is equivalent to two batteries which are connected in parallel having e.m.f.’s 1 E and 2 E and internal resistances 1 r and 2 r respectively are E and r. . (a) 1 1 2 2 1 2 1 2 E r E r E ; r r r (r r ) (b) 1 2 2 1 1 2 1 2 E r E r E ; r r r (r r ) (c) 1 2 2 1 1 2 1 2 1 2 E r E r r r E ; r (r r ) r r (d) 1 1 2 2 1 2 1 2 1 2 E r E r r r E ; r (r r ) r r . V C R1 R2 R3 10. In the circuit shows in figure, the steady state voltage drop across the capacitor is C V . (a) 1 C 2 3 VR V R R (b) 2 C 1 3 VR V R R (c) 1 C 1 2 VR V R R (d) 2 C 1 2 VR V R R . 11. A cell develops same power across two resistors 1 r and 2 r when connected separately. If r is the internal resistance of the cell then (a) 1 2 1 r r r 2 (b) 1 2 r r r (c) 1 2 1 r (r r ) 2 (d) 1 2 r r r .
- 0.5 1.0 1.5 2.0 1 2 3 4 5 V(volt) I(amp) 12. For a cell, a graph is plotted between the potential difference V across the terminals of the cell and the current I drawn from the cell. The e.m.f. and internal resistance of the cell is E and r respectively (a) E = 2 V, r = 0.5 (b) E 2 V, r 0.4 (c) E 2V, r 0.5 (d) E 2V, r 0.4 . G E =5V 2 r =2 2 C B A E =10V 1 r =1 1 13. In the figure the potentiometer wire of length l = 100 cm and resis- tance 9 is joined to a cell of emf 1 E 10V and internal resis- tance 1 r 1 . Another cell of emf 2 E 5V and internal resis- tance 2 r 2 is connected as shown. The galvanometer G will show no deflection when the length AC is: (a) 50 cm (b) 55.55 cm (c) 52.67 cm (d) 54.33 cm. 14. Acapacitor is charged from a cell with the help of a resistor. The circuit has a time constant . The capacitor collects 10% of the steady charge at time t given by (a) ln(1.1) (b) 10 ln 9 (c) ln(0.9) (d) ln(0.1) . 15. Find the reading of the voltmeter (assumed ideal) shown in the diagram V c a d 10 V (a) 8 V (b) 9 V (c) 10 V (d) 6 V.
- OBJECTIVE LEVEL - II A B 4 1. In the given network, the equivalent resistance between A and B is (a) 6 (b) 16 (c) 7 (d) 5 . 2. The equivalent resistance between points A and B is A R B R R R (a) 2R (b) 3 R 4 (c) 4 R 3 (d) 3 R 5 . A B C D H E G F 3. Twelve resistors each of resistance 1 are connected in the cir- - cuit shown in figure. Net resistance between points A and H would be (a) 5 3 (b) 1 (c) 3 4 (d) 7 6 . 4. Which of the following has the maximum resistance? (a) voltmeter (b) galvanometer (c) ammeter (d) miliammeter. 5. A galvanometer of resistance 20 gives a full scale deflection when a current of 0.04 A is passed through it. It is desired to convert it into an ammeter reading 20A in full scale. The only shunt available is 0.05 resistance. The resistance that must be connected in series with the coil of the galvanometer is (a) 4.95 (b) 5.94 (c) 9.45 (d) 12.62 . P 6. A wire of length tapers uniformly from end P to end Q with diameter at P twice that of Q. A potential difference is applied acros the ends of the wire. Which graph represents the drift veloc- ity versus distance from P?
- (a) V l O (b) V l O (c) V l O (d) V l O 7. In the circuit shown in figure reading of voltmeter is 1 V when only 1 S is closed, reading of voltmeter is 2 V when only 2 S is closed and reading of voltmeter is 3 V when both 1 S and 2 S are closed. Then R E 3R 6R s1 s2 V (a) 3 2 1 V V V (b) 2 1 3 V V V (c) 3 1 2 V V V (d) 1 2 3 V V V . 8. Maximumpower developed across resistance R in the circuit shown in figure is 10V R 1 10V 1 (a) 50 watt (b) 75 watt (c) 25 watt (d) 100 watt. 9. Current passing through 3 resistance is A 10V 2 3 B C 4V (a) 14 A 3 (b) 3A (c) 2A (d) 12 A 5 . 10. As the switch S is closed in the circuit shown in figure, current passing through it is 20V 2 4 5V S 2 I2 I1 I (a) 4.5 A (b) 6.0 A (c) 3.0 A (d) zero.
- 11. In the circuit shown in figure A B C F D 4 2V E 2V 4 4 2V (a) current in wire AF is 1A (b) current in wire CD is 1A (c) current in wire BE is 2A (d) none of these. S E R C R 12. In the circuit shown in figure, the switch S is closed at t =0. The voltage across the capacitor C at time t after the switch S is closed is V. The voltage as t is 0 V . (a) 3t /RC E V (1 e ) 3 (b) 0 E V 3 (c) 2t / RC E V (1 e ) 2 (d) 0 E V 4 . 13. In the circuit shown in figure switch S is closed at time t = 0. Let 1 i and 2 i be the currents at any finite time t then the ratio 1 2 i i i1 i2 2C C V R S R (a) is constant (b) increases with time (c) decreases with time (d) first increases and then decreases. R R S E C 14. In the circuit shown, when the switch is closed, the capacitor is charged with time constant 1 and when switch is open, then capacitor discharge with time constant 2 then 1 2 / is : (a) 1 (b) 1 2 (c) 2 (d) 1 4 . 15. The potential difference across the terminals of a battery is 8.5 V when there is a current of 3A in the battery from the negative to the positive terminal. When the current is 2A in the reverse direction, the potential difference becomes 11 V. The internal resistance of the battery is (a) 2.5 (b) 5.5 (c) 2.83 (d) 0.5 .

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