(M=μ 0 πR 2 2 /2R 1 ) (2) 2. Prove that the total inductance of two coils connected in parallel is 1 2 1 1 1 T L L L (2) 3. Define mutual inductance and derive its expression for mutual inductance between two solenoids 4. How is the mutual inductance of a pair of coils affected when a) Separation between the coils is increased, b) the number of turns of each coil is increased, c) a thin sheet of iron is placed between the two coils, other factors remaining the same. Explain your answer in each case. (3) 5. Two circular loops are placed with their centres at fixed distance apart. How would you orient the loops to have (i) maximum (ii) minimum Mutual inductance? (3) 6. A coil of wire of certain radius has 600 turns and inductance of 108mH. What will be the inductance of another similar coil with 500 turns? (3) (75mH) 7. Obtain the mutual inductance of a pair of coaxial circular coils kept separated by a distance as shown in fig:- (3) 8. Prove that for series connection of two coils L T = L 1 +L 2 +2M. (3) Alternating Current RMS current and voltage 1. Find the RMS value of A.C shown in the figure. (1) R r
54 STUDY MATERIAL CLASS XII 2011-12 2. The instantaneous value of e.m.f is given by E= 300sin 314t. What is the rms value of current? Ans:- E 0 =300 units E rms =212.1 units (1) 3. Why a 220 V AC is considered to be more dangerous than 220 V DC? Ans: peak value of AC is more than rms value which is equal to 311V. (1) 4. An AC current flows through a circuit consisting of differerent elements connected in series. (i) Is the applied instantaneous voltages equal to the algebraic sum of instantaneous voltages across the series elements of the circuit? (ii) Is it true for rms voltages? (1) Ans: (i) yes (ii) no 5. A capacitor blocks DC. Why? (1) Ans: X C =1/( 2πfC ), for D.C f=0, therefore X c =α 6. What is the phase relationship between e.m.f across L and C in a series LCR circuit connected to an A.C source? (1) Ans:-The phase difference between V L and V C =180 0 7. What is meant by admittance of an AC circuit? (1) Ans: The reciprocal of impedance is called admittance. 8. Two alternating currents are given by I 1 =I 0 Sinωt and I 2 = I 0 S in(ωt+π/3). Will the rms value of I 1 & I 2 be equal or different? (2) Ans: The rms value will be equal. 9.* An alternating current is given by i=i 1 Cosωt+i 2 Sin ωt. Find the rms current in the circuit . (2) Ans: 2 2 1 2 ( ) / 2 i i 10. An alternating current having a peak value of 14A is used to heat a metal wire. What is the value of steady current which can produce the same heating effect as produced by AC? Why? (2) Ans: i rms =10A 11. If a constant current of 2.8A exists in a resistor, what is the rms value of current? Why? (2) Ans: 2.8A AC Circuits 1. What is meant by wattless current? (1) 2. Define: Q factor in LCR series circuit (1) 3. Why is choke coil preferred over resistor to reduce a.c? (1) 4. How do R, X L and X C get affected when the frequency of applied AC is doubled? (2) Ans: a) R remains unaffected b) X L =2πfL , so doubled c) X C =1/2πfC , so halved
55 STUDY MATERIAL CLASS XII 2011-12 5. For circuits for transporting electric power, a low power factor implies large power loss in transmission line. Why? (2) Ans: rms rms P i V Cos 6. In an AC circuit there is no power consumption in an ideal inductor. Why?
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