Alternating Current- 05-Subjective Unsolved (C.B.S.E.) Level

SUBJECTIVE UNSOLEVED C.B.S.E. LEVEL – I (REVIEW YOUR CONCEPTS) 1. A charged 30 F capacitor is connected to a 27 mH inductor. What is the angular frequency of free oscillations of the circuit ? 2. A series LCR circuit with R = 20  , L = 1.5 H and C = 35 F is connected to a variable-frequency 200 V ac supply. When the frequency of the supply equals the natural frequency of the circuit, what is the average power transferred to the circuit in one complete cycle ? 3. Figure shows a series LCR circuit connected to a variable R frequency 230 V source. L = 5.0 H, C = 80 F , R = 40  . (a) Determine the source frequency, which drives the circuit in  C resonance. (b) Obtain the impedance of the circuit and the amplitude of cur- rent at the resonating frequency. L (c) Determine the rms potential drops across the three elements of the circuit. Show that the potential drop across the LC com- bination is zero at the resonating frequency. 4. An LC circuit contains a 20 mH inductor and a 50 F capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the circuit be closed at t = 0. (a) What is the total energy stored initially ? Is it conserved during LC oscillations ? (b) What is the natural frequency of the circuit ? (c) At what time is the energy stored (i) Completely electrical (i.e., stored in the capacitor) ? (ii) Completely magnetic (i.e., stored in the inductor) ? (d) At what times is the total energy shared equally between the inductor and the capacitor ? (e) If a resistor is inserted in the circuit, how much energy is eventually dissipated as heat ? 5. A coil of inductance 0.50 H and resistance 100  is connected to a 240 V, 50 Hz ac supply. (a) What is the maximum current in the coil ? (b) What is the time lag between the voltage maximum and the current maximum ? 6. A 100 F capacitor in series with a 40  resistance is connected to a 110 V, 60 Hz supply. (a) What is the maximum current in the circuit ? (b) What is the time lag between the voltage maximum and the current maximum ? 7. An ac arc lamp needing 150 volts is put across mains at a pd. of 200 volts and a chocking coil in seris with the lamp. The lamp takes 10 amperes and the frequency is 50 per second. Find (i) the pressure produced by the chocking coil reaction and (ii) the self inductance of the chocking. 8. A circuit containing a 80 mH inductor and a 60 F capacitor in series is connected to a 230 V, 50 Hz supply. The resistance of the circuit is negligible. (a) Obtain the current amplitude and rms values. (b) Obtain the rms values of potential drops across each element. (c) What is the average power transferred to the inductor? (d) What is the average power transferred to the capacitor? (e) What is the total average power absorbed by the circuit ? [‘Average implies ‘averaged over one cycle’] 9. A series LCR circuit with L = 0.12H, C = 480 nF, R = 23  is connected to a 230 V variable frequency supply. (a) What is the source frequency for which current amplitude is maximum. Obtain this maximum value. (b) What is the source frequency for which average power absorbed by the circuit is maximum. Obtain the value of this maximum power. (c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequency ? What is the current amplitude at these frequencies? (d) What is the Q-factor of the given circuit ? 10. A coil of self inductance 0.7 henry is joined in series with a non-inductive resistance of 50  . Calculate the wattles and power components of current when connected to a supply of 200 volts at a frequency of 50 cycles/sec. (Given tan-1 4.4 = 77o 12 )

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