An AC voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series…

An AC voltage source of variable angular frequency $\omega$ and fixed amplitude $V_0$ is connected in series with a capacitance $C$ and an electric bulb of resistance $R$ (inductance zero). When $\omega$ is increased
  1. the bulb glows dimmer
  2. the bulb glows brighter
  3. total impedance of the circuit is unchanged
  4. total impedance of the circuit increases

Solution

$Z=\sqrt{R^2+X_C^2}: I_{\mathrm{rms}}=\frac{V_{\mathrm{rms}}}{Z}: P=I_{\mathrm{rms}}^2 R$ where, $\quad X_C=\frac{1}{\omega C}$ As $\omega$ is increased, $X_C$ will decrease or $Z$ will decrease. Hence $I_{\mathrm{mms}}$ or $P$ will increase. Therefore, bulb glows brighter. Hence the correct option is (b).

Asked in: JEE Advanced 2010 (Paper 1)

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