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**Question 7.1 **A 100 Ω resistor is connected to a 220 V, 50 Hz ac supply.

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

(b) What is the net power consumed over a full cycle?

**Question 7.2**(a) The peak voltage of an ac supply is 300 V. What is the rms voltage?

(b) The rms value of current in an ac circuit is 10 A. What is the
peak current?

**Question 7.3** A 44 mH inductor is connected to 220 V, 50 Hz ac supply. Determine
the rms value of the current in the circuit.

**Question 7.4** A 60 μF capacitor is connected to a 110 V, 60 Hz ac supply. Determine
the rms value of the current in the circuit.

**Question 7.5** In Exercises 7.3 and 7.4, what is the net power absorbed by each
circuit over a complete cycle. Explain your answer.

**Question 7.6** Obtain the resonant frequency ωr of a series LCR circuit with
L = 2.0H, C = 32 μF and R = 10 Ω. What is the Q-value of this circuit?

**Question 7.7** A charged 30 μF capacitor is connected to a 27 mH inductor. What is
the angular frequency of free oscillations of the circuit?

**Question 7.8** Suppose the initial charge on the capacitor in Exercise

**Question 7.7** is 6 mC.
What is the total energy stored in the circuit initially? What is the
total energy at later time?

**Question 7.9** A series LCR circuit with R = 20 Ω, L = 1.5 H and C = 35 μF 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?

**Question 7.10** A radio can tune over the frequency range of a portion of MW
broadcast band: (800 kHz to 1200 kHz). If its LC circuit has an effective
inductance of 200 μH, what must be the range of its variable
capacitor?
[Hint: For tuning, the natural frequency i.e., the frequency of free
oscillations of the LC circuit should be equal to the frequency of the
radiowave.]

**Question 7.11** Figure 7.21 shows a series LCR circuit connected to a variable
frequency 230 V source. L = 5.0 H, C = 80μF, R = 40 Ω.

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

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

(c) Determine the rms potential drops across the three elements of
the circuit. Show that the potential drop across the LC
combination is zero at the resonating frequency.

ADDITIONAL EXERCISES QUESTIONS

**Question 7.12 **An LC circuit contains a 20 mH inductor and a 50 μF 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
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?

**Question 7.13** A coil of inductance 0.50 H and resistance 100 Ω 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?

**Question 7.14** Obtain the answers (a) to (b) in Exercise 7.13 if the circuit is
connected to a high frequency supply (240 V, 10 kHz). Hence, explain
the statement that at very high frequency, an inductor in a circuit
nearly amounts to an open circuit. How does an inductor behave in
a dc circuit after the steady state?

**Question 7.15** A 100 μF capacitor in series with a 40 Ω 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 current maximum and the
voltage maximum?

**Question 7.16** Obtain the answers to (a) and (b) in Exercise 7.15 if the circuit is
connected to a 110 V, 12 kHz supply? Hence, explain the statement
that a capacitor is a conductor at very high frequencies. Compare this
behaviour with that of a capacitor in a dc circuit after the steady state.

**Question 7.17** Keeping the source frequency equal to the resonating frequency of
the series LCR circuit, if the three elements, L, C and R are arranged
in parallel, show that the total current in the parallel LCR circuit is
minimum at this frequency. Obtain the current rms value in each
branch of the circuit for the elements and source specified in
Exercise 7.11 for this frequency.

**Question 7.18** A circuit containing a 80 mH inductor and a 60 μF 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’.]

**Question 7.19** Suppose the circuit in Exercise 7.18 has a resistance of 15 Ω. Obtain
the average power transferred to each element of the circuit, and
the total power absorbed.
Physics
268

**Question 7.20** 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 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?

**Question 7.21** Obtain the resonant frequency and Q-factor of a series LCR circuit
with L = 3.0 H, C = 27 μF, and R = 7.4 Ω. It is desired to improve the
sharpness of the resonance of the circuit by reducing its ‘full width
at half maximum’ by a factor of 2. Suggest a suitable way.

**Question 7.22** Answer the following questions:

(a) In any ac 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 rms 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 dc voltage
and an ac voltage of high frequency. The circuit consists of an
inductor and a capacitor in series. Show that the dc signal will
appear across C and the ac signal across L.

(d) A choke coil in series with a lamp is connected to a dc 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 ac line.

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

**Question 7.23** A power transmission line feeds input power at 2300 V to a stepdown
transformer with its primary windings having 4000 turns. What
should be the number of turns in the secondary in order to get output
power at 230 V?

**Question 7.24** At a hydroelectric power plant, the water pressure head is at a height
of 300 m and the water flow available is 100 m3s–1. If the turbine
generator efficiency is 60%, estimate the electric power available
from the plant (g = 9.8 ms–2 ).

**Question 7.25 **A small town with a demand of 800 kW of electric power at 220 V is
situated 15 km away from an electric plant generating power at 440 V.
The resistance of the two wire line carrying power is 0.5 Ω per km.
The town gets power from the line through a 4000-220 V step-down
transformer at a sub-station 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) Characterise the step up transformer at the plant.

**Question 7.26** Do the same exercise as above with the replacement of the earlier
transformer by a 40,000-220 V step-down transformer (Neglect, as
before, leakage losses though this may not be a good assumption
any longer because of the very high voltage transmission involved).
Hence, explain why high voltage transmission is preferred?

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- Chapter 1: ELECTRIC CHARGES AND FIELDS
**[Ques wise Ans]** - Chapter 1 Electric Charges and Fields
- Chapter 2 Electrostatic Potential and Capacitance
- Chapter 3 Current Electricity
- Chapter 4 Moving Charges and Magnetism
- Chapter 5 Magnetism and Matter
- Chapter 6 Electromagnetic Induction
- Chapter 7 Alternating Current
- Chapter 8 Electromagnetic Waves
- Chapter 9 Ray Optics and Optical Instruments
- Chapter 10 Wave Optics
- Chapter 11 Dual Nature of Radiation and Matter
- Chapter 12 Atoms
- Chapter 13 Nuclei
- Chapter 14 Semiconductor Electronics: Materials, Devices and Simple Circuits
- Chapter 15 Communication Systems

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