# NCERT 12 Physics Alternating Currents Chapter 7 Exercise

Q.1. A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.220

(a) What is the rms value of current in the circuit ?

(b) What is the net power consumed over a full cycle ? Q.2. (a) The H inductor is connected to 220 V, 50 Hz a. c. supply. Determine the r. m. s. voltage ?

(b) The r. m. s. value of current in an ac circuit is 10 A. What is the peak current ? Q.3. A 44 m H inductor is connected to 220 V, 50 Hz a. c. supply. Determine the r. m. s. value of current in the circuit. Q.4. A 60  capacitor is connected to a 110 V, 60 Hz a. c. supply. Determine the r. m. s. value of current in the circuit. Q.5. In Questions 3 and 4, what is the net power absorbed by earth circuit over a complete cycle ? Explain your answer. Infact, in both the cases, power spent in one half cycle is retrieved in the other half cycle.

Q.6. Obtain the resonant frequency ( of a series LCR circuit with L  =  2.0 H,C = 32  What is the  value of this circuit ? Q.7. A charged 30  capacitor is connected to a 27 m H inductor. What is the angular frequency of free oscillations of the circuit ? Q.8. Suppose the initial charge on the capacitor in the above question is 6 mC. What is the total energy stored in the capacitor initially ? What is the total energy at later time ? At later times, energy is shared between C and L, but total energy remains the same, assuming that there is no loss of energy.

Q.9. A series LCR circuit with R = 20 L = 1.5 H and C = 35 is connected to a variable frequency 200 V a. c. supple. 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 ?

Sol. When the frequency of the supply equals the natural frequency of the circuit, resonance occurs. Q.10. A radio can tune over the frequency range of a portion of portion of MW broadcast band (800 kHz to 1200 . If its LC circuit has an effective inductance of 200 , what must be the range of its variable capacitor ? Q.11. A series LCR circuit connected to a variable frequency 230 V source has  L  = 5.0 H, C  =  80 , R = 40 Ω,

(a) Determine the source frequency which drives the circuit in resonance.

(b) Obtain the impedance of the circuit and amplitude of current at the resonating frequency.

(c) Determine the r. m. s. potential drops across the three elements of the circuit. Show that the potential drop across the LC combination is zero at the resonating frequency.   Q.12. An LC circuit contains a 20 mH inductor and a 50  capacitor with an initial charge of 10 mC. The resistance of the circuit is negligible. Let the instant the circuit is closed be  t = 0.

(a) What is the total energy stored initially ? Is it conserved during the oscillalions ?

(b) What is the natural frequency of the circuit ?

(c) At what time is the energy stored ? (i) Completely electrical? (ii) Completely magnetic ?

(d) At what time 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 ?  (e) The presence of resistor in the circuit involves loss of energy. The oscillation become damped and ultimately they disappear. When total energy of 1 joule is dissipated as teat.

Q.13. A coli of inductance 0.50 H and resistance 100  is connected to a 240 V, 50 Hz a.c. supply.

(a) What is the maximum current in the coli ?

(b) What is the time lag between the voltage maximum and current maximum ? Q.14. Obtain the answers to (a) and (b) in Q.13 of the circuit is connected to a high frequency supply (240 V, 10 kHz). Hence explain statement that at very high frequency, inductor in circuit nearly amounts to open circuit. How does an inductor behave in a d.c. circuit after the steady state ? On contribute, we find that at low frequencies,

At high frequencies,

At high frequencies, L offers very high resistance which amounts to an open circuit (infinite resistance). In a d c circuit, after steady state,  Therefore, XL =  Hence L acts like a pure conductor of negligible inductive reactance. It has no role to play.

Q.15. A 100  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 current maximum and voltage maximum ? Q.16. Obtain the answers to (a) and  (b) in Q.15, if the circuit is connected to 110 V, 12 kHz supply. Hence explain the statement that a capacitor is a conductor at very high frequencies. Compare this behavior with that of a capacitor in d. c. circuit after the steady state. Here, contribution of term containing C is negligible.

In the RC circuit, voltage lags behind the current by a phase angle ф, where Therefore, behaviour of capacitor towards d. c. amounts to an open circuit.

Q.17. Keeping the source frequency equal to the resonating frequency of the series LCR circuit, if the three elements L, C and R in Q.11, are arranged in parallel, show that the total current in the parallel LCR circuit is a minimum at this frequency. Obtain the r. m. s. value of current in each branch of the circuit for the elements and source specified in Q. 11 for this frequency.

Sol. If Z is the effective impedance of the parallel LCR circuit shown in then in vector form,   Q.18. 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 in the circuit is negligible.

(a) Obtain the current amplitude and r. m. s. value.

(b) Obtain the r. m. s. values of potential drop across each element.

(c) What is the average power transferred to inductor ?

(d) What is the average power transferred to capacitor ?

(e) What is the total average power absorbed by the circuit? [‘Average’ implies ‘averaged over one cycle’].  (c) Average power transferred over a complete cycle by the source to inductor in always zero because of phase difference of /2 between voltage and current through L.

(d) average power transferred over a complete cycle by the source to the capacitor is also zero because of phase difference of /2 between voltage and current through C.

(e) Total average power absorbed by the circuit is also, through zero.

Q.19. Suppose the circuit in Q.18 has a resistance of 15 ohm. Obtain the average power transferred to each element of the circuit, and the total power absorbed. Average power per cycle transferred to resistance

Average power per cycle transferred to L  =  PL = 0

Average power per cycle transferred to L  =  PL =PC =  0

Total power per cycle absorbed, P = PR + PL + PC = 790.6 watt

Q.20. A series LCR circuit with  L  =  0.12 H, C = 480 nF , R = 23 Ω 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 max. power.

(c) For which frequencies of the source is the power transferred to the circuit half the power at resonant frequencies. What is the current amplitude at these frequencies ?

(d) What is the Q factor of the given circuit ?  Q.21. Obtain the resonant frequency and Q- factor of a series LCR circuit with  L  =  3.0 H, C = 27  F and R =  7.4 Ω. It is desired to improve the sharpness of resonance of the circuit by reducing its full width at half max. by factor of 2. Suggest a suitable way. Q.22. Answer the following questions :

(a) In any a. c. circuit, is the applied instantaneous voltage equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit ? Is the same true for r. m. s. voltage ?

(b) A capacitor is used in the primary circuit of an induction coil.

(c) An applied voltage signal consists of a superposition of a d. c. voltage and an a. c. voltage of high frequency. The circuit consists of an inductor and a capacitor in series. Show that the d. c. signal will appear across C and the a. c. signal will appear across L.

(d) A choke coil in series with a lamp is connected to a d. c. line. The lamp is seen to shine brightly. Insertion of an iron core in the choke causes no change in the lamp’s brightness. Predict the corresponding observations if the connection is to an a. c. line.

(e) Why is choke coil needed in the use o fluorescent tubes with ac mains ? Why can we not use an ordinary resistor of choke coil ?

Sol. (a) Yes, applied instantaneous voltage is always equal to the algebraic sum of the instantaneous voltages across the series elements of the circuit.

No, this is not true in case of r. m. s. voltages, because such voltages across different elements may not be in same phase.

(b) When the circuit is broken, the large induced voltage is used up in capacitor. Thus sparking etc. is avoided. Inductor blocks it. Hence a. c. signal appears across L.

(d) On a d. c. line, choke has no impedance. Therefore, lamp shines brightly and there is no effect of inserting iron core is inserted in the choke, its impedance to a. c. increases further. Therefore, brightness of the bulb decreases.

(e) A choke coil is needed in the use of fluorescent tubes to reduce ac without loss of power. If we use an ordinary resistor, ac will reduce, but loss of power due to heating will be there. Q.23. A power transmission line feeds input power at 2300 V to a step down transformer, with its primary windings having 4000 turns. What should be the number of turns in the secondary windings in order to get output power at 230 V ? Q.24. At a hydroelectric power plant, the water pressure head is at a height of 300 m and the water flow available is 100 m3 s-1 . If the turbine generator efficiency is 60, estimate the electric power available from the plant (g  = 9.8 ms-2 ). Q.25. A small town with a demand of 800 kW of electric power at 2.20 V is situated 15 km away from an electric plant generating power at 440 V. The resistance of the two line wires carrying power is 0.5 Ω per km. The town gets power from the lines through a 4000220 V step down transformer at a substation in the town.

(a) Estimate the line power loss in the form of heat.

(b) How much power must the plant supply, assuming there is negligible power loss due to leakage?

(c) Characterize the step up transformer at the plant. Q.26. Do Q.25 fiven abve with the replacement of earlier transformer by 40000 – 220 V step down transtormer. Neglect as before, leakage losses. Hence explain why high voltage transmission is preferred. Updated: May 2, 2022 — 9:50 pm