Page 46 - Physics - XII

Q9. An alternating current is given i = i cos ωt + i sin ωt. The rms current is given by
1
2
i + i i − i i + i 2 ii
2
(a) 1 2 (b) 1 2 (c) 1 2 (d) 12
2 2 2 2

200 1
Q10. An A.C. source is of V, 50 Hz. The value of voltage after s from the start is
2 600

(a) 200 V (b) 200 V (c) 100 V (d) 50 V
2
Answer key

1. (b), 2. (a), 3. (a), 4. (b), 5. (b), 6. (c), 7. (c), 8. (d), 9. (c), 10. (c)

Case Study-based Questions

Read the paragraph and answer the questions that follow.

An interesting characteristic of the series RLC circuit is the phenomenon of resonance. The phenomenon
of resonance is common among systems that have a tendency to oscillate at a particular frequency. This
frequency is called the system’s natural frequency. If such a system is driven by an energy source at a

frequency that is near the natural frequency, the amplitude of oscillation is found to be large. A familiar
example of this phenomenon is a child on a swing. The swing has a natural frequency for swinging back
and forth like a pendulum. If the child pulls on the rope at regular intervals and the frequency of the pulls
is almost the same as the frequency of swinging, the amplitude of the swinging will be large.

Suppose a resistance R, inductance L, and capacitance C are connected in series and fed by an alternating
source of voltage V, the frequency of alternating current source be f. This series RLC circuit is said to be
in resonance only if the frequency f of applied alternating source be such that the current fl owing in circuit
and voltage applied are in the same phase. At resonance in RLC series circuit impedance is minimum

(i.e. Z = R). For an RLC circuit driven with voltage of amplitude V , the angular frequency ω is given by
0
m
1
ω =
0 LC
At resonant frequency, the current amplitude is maximum

V
i.e. i = R m
m
Q1. To reduce the resonant frequency in an LCR series circuit with a generator,

(a) the generator frequency should be reduced.
(b) another capacitor should be added in parallel to the fi rst.

(c) the iron core of the inductor should be removed.

(d) dielectric in the capacitor should be removed.

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