A capacitor, an inductor and an electric bulb are connected in series to an a.c. supply of variable…

A capacitor, an inductor and an electric bulb are connected in series to an a.c. supply of variable frequency. As the frequency of the supply is increased gradually, then the electric bulb is found to
  1. increase in brightness.
  2. decrease in brightness.
  3. increase, reach a maximum and then decrease in brightness
  4. show no change in brightness.

Solution

The given circuit acts like a series LCR circuit $I=\frac{V}{Z}=\frac{V}{\sqrt{R_2+\left(\omega L-\frac{1}{\omega C}\right)^2}}$ From the above formula, when $\omega=0$, $\mathrm{I}=$ maximum When $\omega$ is increased, I starts to decrease and when $\omega=\frac{1}{\sqrt{\mathrm{LC}}}$ the current will be zero. This cycle will repeat going forward. So brightness will increase, reach a maximum and then decrease. .

Asked in: MHT CET 2023 (09 May Shift 1)

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