JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Alternating Current

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A series R-C 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) $I_{R}^{A} < I_{R}^{B}$ ✓ Correct
(C) $V_{C}^{A} > V_{C}^{B}$ ✓ Correct
(D) $V_{C}^{A} < V_{C}^{B}$

Answer: (B), (C)

Solution

When dielectric (K=4) is inserted, capacitance increases:

C_{B} = 4 C_{A}

. Impedance

Z = R^{2} + \frac{1}{( ω C ) ^{2}}

decreases as C increases, so current increases:

I_{R}^{A} < I_{R}^{B}

. Voltage across capacitor

V_{C} = \frac{I}{ω C}

. Since

I_{B} > I_{A}

but

C_{B} = 4 C_{A}

, the ratio

\frac{I}{C}

decreases, giving

V_{C}^{A} > V_{C}^{B}

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JEE Advanced · 2011 · 10 Apr 2011 · Paper 2 · Alternating Current

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