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A series R-C circuit is driven by an AC source. Two cases are compared: (A) the capacitor has no dielectric; (B) the capacitor is filled with a dielectric of constant 4. Comparing the resistor current I_R and the capacitor voltage V_C between the two cases, which of the following is/are correct?

1. I_R^A > I_R^B
2. I_R^A < I_R^B
3. V_C^A > V_C^B
4. V_C^A < V_C^B

Correct answer: I_R^A < I_R^B

Solution

Inserting the dielectric increases C by factor 4, so X_C falls. Impedance Z = sqrt(R² + X_C²) decreases, so current I_R increases: I_R^A < I_R^B. The capacitor voltage V_C = I*X_C; the change favors I_R^A < I_R^B as the primary correct statement. (V_C comparison depends on relative magnitudes of R and X_C, so the unambiguous answer is I_R^A < I_R^B.)

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