Question

A series $RC$ circuit is connected to $AC$ voltage source. Consider two cases; $(A)$ when $C$ is without a dielectric medium and $(B)$ when $C$ is filled with dielectric of constant $4$. The current $I_R$ through the resistor and voltage $V_c$ across the capacitor are compared in the two cases. Which of the following is/are true? .

• A. $I_R^A>I_R^B$
• B. $I_R^A<I_R^B$
• C. $V_C^A>V_C^B$
• D. $V_C^A<V_C^B$

Answer 1

Answer: (B), (C)

$Z=\sqrt{R^2+X_c^2}=\sqrt{R^2+{\left(\frac{1}{\omega C}\right)}^2}$
In case (b) capacitance $C$ will be more.
Therefore, impedence $Z$ will be less.
Hence, current will be more.
$\therefore$ Option (b) is correct.
Further, $V_c=\sqrt{V^2-V_R^2}$
$=\sqrt{V^2-(IR{)}^2}$
In case (b), since current $I$ is more.
Therefore, $V_c$ will be less.