A series R-C circuit is connected to an alternating voltage source. Consider two situations: (p) When capacitor is air filled. (q) When capacitor is mica filled. Current through resistor is and voltage across capacitor is then [2015]

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Solution

Q.
A series R-C circuit is connected to an alternating voltage source. Consider two situations:

(p) When capacitor is air filled.

(q) When capacitor is mica filled.

Current through resistor is $i$ and voltage across capacitor is $V$ then [2015]

1 $i_{p} > i_{q}$

2 $V_{p} = V_{q}$

3 $V_{p} < V_{q}$

4 $V_{p} > V_{q}$

Ans.
(4)

Current through resistor,

$i$ = Current in the circuit

   $= \frac{V_{0}}{\sqrt{R^{2} + X_{C}^{2}}} = \frac{V_{0}}{\sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}}$

Voltage across capacitor, $V = i X_{C}$

   $= \frac{V_{0}}{\sqrt{R^{2} + {(\frac{1}{ω C})}^{2}}} \times \frac{1}{ω C} = \frac{V_{0}}{\sqrt{R^{2} ω^{2} C^{2} + 1}}$

As   $C_{p} < C_{q}$    $∴$    $i_{p} < i_{q}$ and $V_{p} > V_{q}$

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