An AC voltage source of variable angular frequency $\omega$ and fixed amplitude $\mathrm{V}_{\mathrm{o}}$ is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When $\omega$ is increased

(C) total impedance of the circuit is unchanged

(D) total impedance of the circuit increases

JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Alternating Current

An AC voltage source of variable angular frequency

ω

and fixed amplitude

V_{o}

is connected in series with a capacitance C and an electric bulb of resistance R (inductance zero). When

ω

is increased

(A)the bulb glows dimmer
(B)the bulb glows brighter✓ Correct
(C)total impedance of the circuit is unchanged
(D)total impedance of the circuit increases

Answer: (B)

Solution

The impedance of the RC series circuit is

Z = R^{2} + X_{C}^{2}

, where

X_{C} = 1/ (ω C)

is the capacitive reactance. As

ω

increases,

X_{C}

decreases, so

Z

decreases. With fixed voltage

V_{0}

, the current

I = V_{0} / Z

increases. The power dissipated in the bulb is

P = I^{2} R

, which increases, making the bulb glow brighter. The answer is (B).

JEE Advanced · 2010 · 11 Apr 2010 · Paper 1 · Single correct option

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