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

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7.Alternating Current

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

$(a)$ When capacitor is air filled.

$(b)$ When capacitor is mica filled.

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

A

$V_a=V_b$

B

$V_a< V_b$

C

$V_a > V_b$

D

$i_a >i_b$

(AIPMT-2015)

Solution

Current through resistor, $i$

$=$ Current in the circuit

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

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

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

As ${C_a} < {C_b}$

$\therefore \,\,{i_a} < {i_b}$ and ${V_a} < {V_b}$

Standard 12

Physics

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(AIIMS-2011)