A series R-C circuit is connected to an alternating voltage source. Consider two situations: 1. When the capac

Question

A series R-C circuit is connected to an alternating voltage source. Consider two situations: 1. When the capacitor is air-filled. 2. When the capacitor is mica filled. If the current through the resistor is $I$ and voltage across the capacitor is $V$, then:

Accepted Answer

1. **Capacitance:** When a dielectric like mica (with dielectric constant $K > 1$) fills the capacitor, the capacitance increases from $C_a$ to $C_b = K C_a$ .
2. **Reactance:** Capacitive reactance is inversely proportional to capacitance ($X_C = 1/\omega C$). Since $C$ increases, $X_C$ decreases ($X_{C,b} < X_{C,a}$) .
3. **Impedance and Current:** The total impedance $Z = \sqrt{R^2 + X_C^2}$ decreases. Consequently, the current in the circuit $I = V_{source}/Z$ increases ($I_b > I_a$).
4. **Voltage across Capacitor:** The voltage across the capacitor is given by $V_C = I X_C = \frac{V_{source} X_C}{\sqrt{R^2 + X_C^2}} = \frac{V_{source}}{\sqrt{(R/X_C)^2 + 1}}$. As $C$ increases, $X_C$ decreases, causing the term $(R/X_C)$ to increase. This increases the denominator, thereby decreasing the voltage across the capacitor. Thus, $V_a > V_b$.

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