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  4. 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 IR through the resistor and voltage Vc across the capacitor are compared in the two cases. Which of the following is/are true? .

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Q. 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? .

IIT JEEIIT JEE 2011Alternating Current

Solution:

$Z=\sqrt{R^{2}+X_{c}^{2}}=\sqrt{R^{2}+\left(\frac{1}{\omega C}\right)^{2}}$
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, $V_{c}=\sqrt{V^{2}-V_{R}^{2}}$
$=\sqrt{V^{2}-(I R)^{2}}$
In case (b), since current $I$ is more.
Therefore, $V_{c}$ will be less.