Title 13-emi-and-ac-circuits-.pdf ✅

EMI and AC Circuits 1. Two ends of an inductor of inductance L are connected to two parallel conducting wires. A rod of length l and mass m is given velocity v0 as shown. The whole system is placed in perpendicular magnetic field B. Find the maximum current in the inductor. (Neglect gravity and friction) (A) mv0 L (B) √ m L v0 (C) mv0 2 L (D) None of these 2. A rod is rotating with a constant angular velocity ω about point O (its centre) in a magnetic field B as shown. Which of the following figure correctly shows the distribution of charge inside the rod? (A) (b) (C) (d)
3. In the figure magnetic field points into the plane of paper and the conducting rod of length l is moving in this field such that the lowest point has a velocity v1 and the top most point has the velocity v2 (v2 > v1 ). The emf induced is given by : (A) Bv1l (B) Bv2l (C) 1 2 B(v2 + v1 )l (D) 1 2 B(v2 − v1 )l 4. A metallic ring of mass m and radius r with a uniform metallic spoke of same mass m and length r is rotated about its axis with angular velocity ω in a perpendicular uniform magnetic field B as shown. The central end of he spoke is connected to the rim of the wheel through a resistor R as shown. The resistor does not rotate, its one end is always at the centre of the ring and other end is always in contact with the ring. A force F as shown is needed to maintain constant angular velocity of the wheel. F is equal to (the ring and the spoke has zero resistance) : (A) B 2ωr 2 8R (B) B 2ωr 2 2R (C) B 2ωr 3 2R X (D) B 2ωr 3 4R 5. A closed circuit consists of a resistor R, inductor of inductance L and a source of emf E connected in series. If the inductance of the coil is abruptly decreased to L/4 (by removing its magnetic core), the new current immediately after this moment is : (before decreasing the inductance the circuit is in steady state) (A) zero (B) E/R (C) 4 E R (D) E 4R 6. A small circular wire loop of radius a is located at the centre of a much larger circular wire loop of radius b as shown ( b > a ). Both loops are coaxial and coplanar. The larger loop carries a time (t) varying current I = I0cos ωt, where I0 and ω are constants. The magnetic field generated by the current in the large loop induces in the small loop an emf that is approximately equal to which of the following ?
(A) πμ0I0a 2 2b ωcos ωt (B) πμ0I0a 2 2b ωsin ωt (C) πμ0I0a 2b2 ωsin ωt (D) πμ0I0 2b2 ωcos ωt 7. A square loop of side a and a straight long wire are placed in the same plane as shown in figure. The loop has a resistance R and inductance L. The frame is turned through 180∘ about the axis OO′ . What is the electric charge that flows through the loop? (A) μ0Ia 2πR ln ( 2a+b b ) (B) μ0Ia 2πR ln ( b b2−a2 ) (C) μ0Ia 2πR ln ( a+2b b ) (D) None of these 8. A flat coil of area A and n turns is placed at the centre of ring of radius r(r 2 ≫ A) and resistance R. The two are coplanar. When current in the coil is increased from zero to i, the total charge circulating in the ring is : (A) μ0nAi 2rR (B) μ0n 2Ai 2rR (C) μ0nAi 2πr (D) μ0n 2Ai 4πrR 9. PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity V as shown. The force needed to maintain constant speed of EF is : (A) 1 VR [ μ0IV 2π ln ( b a )] 2 (B) [ μ0IV 2π ln ( b a )] 1 R (C) [ μ0IV 2π ln ( b a ) 2 ] V R (D) [ μ0IV 2π ln ( b a )] 10. Figure shows a square loop of side 1 m and resistance 1Ω. The magnetic field on left side of line PQ has a magnitude B = 1.0 T. The work done in pulling the loop out of the field uniformly in 1 s is : (A) 1 J (B) 10 J (C) 0.1 J (D) 100 J 11. An inductor L and a resistor R are connected in series with a direct current source of emf E. The maximum rate at which energy is stored in the magnetic field is : (A) E 2 4R (B) E 2 R (C) 4E 2 R (D) 2E 2 R
12. If the reading of v1 and v3 are 100 volt each then reading of v2 is: (A) 0 volt (B) 100 volt (C) 200 volt (D) cannot be determined by given information 13. What is the amount of power delivered by the ac source in the circuit shown (in watts)? (A) 500 watt (B) 1014 watt (C) 1514 watt (D) 2013 watt 14. Consider a pair of smooth metallic rails joined at one of the ends. Rails are parallel and are inclined at 30∘ with horizontal. A jumper of mass m, length l and resistance R slides down the rails with constant speed v. Magnetic field in the region is vertical. Strength of magnetic field is : (A) √ mgR 3vl 2 (B) √ 2mgR 3vl 2 (C) √ 3mgR vl 2 (D) √ √3mgR vl 2 15. For the circuit shown here, keys k1 and k3 are closed for 1 second. Now keys k1 and k3 are opened and key k2 is closed at the same instant. Maximum charge on the capacitor after key k2 is closed is : (A) 4 (1 − 1 e ) C (B) 4√2 (1 − 1 e ) C (C) 8 (1 − 1 e ) C (D) Zero 16. In the circuit shown, the reading of ammeter is 10 A and that of VC = 200 V. The reading of VL is : (A) 200 V (B) 200√2V (C) (−200 + 1000√2)V (D) Zero