Title 11--dc-circuits-and-capacitors-.pdf ✅

DC Circuits and Capacitors 1. If certain number of bulbs rated as ( P1 watt, V volt), (P2 watt, V volt) ......are connected in series across a potential difference of V volt, then power ' P ' consumed by all bulbs is given as: (A) P = P1 + P2 + P3 (B) 1 P = 1 P1 + 1 P2 + 1 P3 ... ... .... (C) P 2 = P1 2 + P2 2 + P3 2 (D) None of these 2. In the given circuit, the galvanometer G will show zero deflection if: (A) R1R2 = R3R4 (B) R1R3 = R2R4 (C) R1R4 = R2R3 (D) none of the above 3. Two scales on a voltmeter measure voltages up to 20.0 V and 30.0 V. The resistance connected in series with the galvanometer is 1680Ω for the 20.0 V scale and 2930Ω for the 30.0 V scale. The resistance of the galvanometer and the full scale current are respectively (A) 320Ω and 8 mA (B) 70Ω and 10Ma (C) 820Ω and 10 mA (d) 820Ω and 8 mA 4. The equivalent resistance between A and B in the arrangement of resistance, as shown, is : (A) 4r (B) 3r (C) 2.5r (D) r 5. A conductor of resistivity ρ and resistance R, as shown in the figure, is connected across a battery of emf V. Its radius varies from 'a' at left end to ' b ' at right end. The electric field at a point P at distance x from left end of it is: (A) Vl 2ρ πR(la+(b−a)x) 2 (B) 2Vl 2ρ πR(la+(b−a)x) 2 (C) Vl 2ρ 2πR(la+(b−a)x) 2 (D) none of these 6. A piece of conducting wire of resistance R is cut into 2n equal parts. Half the parts are connected in series to form a bundle and remaining half in parallel to form another bundle. These bundles are then connected to give the maximum resistance. The maximum resistance of the combination is (A) R 2 (1 + 1 n2 ) (B) R 2 (1 + n 2 ) (C) R 2(1+n2) (D) R (n + 1 n ) 7. A milli ammeter of range 5 mA and resistance 0.5Ω is joined in a circuit as shown. Find the value of current for which meter gives full scale deflection when A and B are used as terminals :
(A) 50 mA (B) 5 mA (C) 100 mA (D) 1 A 8. Two batteries one of emf 3 V, internal resistance 1ohm and the other of emf 15 V, internal resistance 2 ohm are connected in series with a resistance R as shown. If the p.d. between a and b is zero, the resistance of R in ohm is: (A) 5 (B) 7 (C) 3 (D) 6 9. In the circuit segment shown, the potential difference VB − VA = 11 V at an instant when the Q = 16μC. What can be said about the capacitor at this instant? (A) it is absorbing power at the rate of 20 mW (B) it is delivering power at the rate of 9.3 mW (C) it is delivering power at the rate of 20 mW (D) it is absorbing power at the rate of 9.3 mW 10. In the given circuit, the capacitor of capacitance C is charged by closing key K at t = 0. Find the time required to charge the capacitor upto maximum charge for the given circuit, if it were to be charged with the constant initial charging rate at t = 0 in the given circuit. (A) RC 3 (B) 2RC 5 (C) 2RC 3 (D) 5RC 3 11. A metal sphere of radius ' a ' is surrounded by a concentric metal sphere of radius ' b ' ( b > a). The space between the spheres is filled with a material whose electrical conductivity σ varies with the electric field strength E according to relation σ = kE, where k is a constant. A potential difference V is maintained between two spheres. The current between the spheres is: (A) [ 4πkV 2 {ln (b/a)} 2 ] (B) [ 2πkV 2 {ln (b/a)} 2 ] (C) [ πkV 2 4{ln(b/a)} 2 ] (D) [ 8πkV 2 {lln (b/a)} 2 ] 12. Charge on capacitor in steady state : (A) CV (B) CV/2 (C) CV (1 − 1 2R ) (D) Zero 13. From a supply of identical capacitors rated 8μF, 250 V, the minimum number of capacitors required to form a composite 16μF, 1000 V capacitor is : (A) 2 (B) 4 (C) 16 (D) 32 14. Five identical capacitor plates are arranged such that they make four capacitors each of 2μF. The plates are connected to a source of emf. 10 V. The charge on plate C is
(A) + 20μC (B) + 40μC (C) + 60μC (D) + 80μC 15. The plates of a parallel plate capacitor are given surface charge densities +σ, −σ. A dielectric slab of dielectric constant ' ε ' is introduced between the plates. If the area of plates is A, then the force by a capacitor plate on the facing dielectric surface is : (A) σ 2 (ε−1)A ε0 2 (B) σ 2 (ε−1)A 2ε0ε (C) σ 2 (ε−1)A 2ε0 (D) σ 2 (ε−1)A 2ε0 2 MULTIPLE CORRECT ANSWERS TYPEEach of the following Question has 4 choices A, B, C & D, out of which ONE or MORE Choices may be Correct: 16. A source of constant potential difference is connected across a conductor having irregular cross-section as shown in figure. Then: (A) Electric field intensity at P is greater than that at Q (B) Rate of electrons crossing per unit area of cross- section at P is less than that at Q (C) The rate of generation of heat per unit length at P is greater than that at Q (D) Mean kinetic energy of free electron at P is greater than that at Q 17. In the figure, a conductor of non-uniform cross- section is shown. A steady current I flows in it. (A) The electric field at A is more than at B. (B) The electric field at B is more than at A. (C) The thermal power generated at A is more than at B in an element of small width. (D) The thermal power generated at B is more than at A in an element of small width. 18. Potential difference between points A and B (i.e. VA − VB ) is (A) 4 V (B) 6 V (C) − 4 V (D) −6 V 19. In the potentiometer circuit of given figure, the galvanometer reveals a current in the direction shown wherever the sliding contact touches the wire. This could be caused by (A) E1 being too low (B) r being too high (C) a break in PQ (D) E2 being too low 20. The galvanometer shown in the figure has resistance 10Ω. It is shunted by a series combination of a resistance S = 1Ω and an ideal cell of emf 2 V. A current 2 A passes as shown. Then:
(A) The reading of the galvanometer is 1 A (B) The reading of the galvanometer is zero (C) The potential difference across the resistance S is 1.5 V (D) The potential difference across the resistance S is 2 V 21. In the circuit shown in figure, E1 and E2 are two ideal sources of unknown emfs. Some currents are shown. Potential difference appearing across 6Ω resistance is VA − VB = 10 V. (A) The current in the 4.00Ω resistor is 5 A. (B) The unknown emf E1 is 36 V. (C) The unknown emf E2 is 54 V. (D) The resistance R is equal to 9Ω. 22. In the circuit shown, R1 = R2 = 10Ω and resistance per unit length of wire PQ = 1Ω/cm and length PQ = 10 cm. If R2 is made 20Ω then to get zero deflection in galvanometer: ( S is midpoint of wire PQ ). (A) The jockey at P can be moved towards right 2 cm. (B) The jockey at Q can be moved towards right 2 cm. (C) The jockey at S can be moved towards left a distance 5/3 cm. (D) The jockey at all positions fixed and R1 should be made 20Ω. 23. The diagram shows a modified meter bridge, which is used for measuring two unknown resistance at the same time. When only the first galvanometer is used, for obtaining the balance point, it is found at point C. Now the first galvanometer is removed and the second galvanometer is used, which gives balance point at D. Using the details given in the diagram, find out the value of R1 and R2. (A) R1 = 5R/3 (C) R1 = 4R/3 (B) R2 = 4R/3 (D) R2 = 5R/3 AB = L; AC = L/4 and AD = 2l 3 24. Choose the correct statement(s) : (A) The 10 V battery is getting discharged (B) The 5 V battery is getting charged (C) The 5 V battery is getting discharged (D) The 10 V battery is getting charged 25. If the switch at point P is opened (shown in the figure), choose the correct option: