A series `R-C` circuit is connected to an alternating voltage source. Consider two situations
(a) When capacitor is air filled.
(b) When capacitor is mica filled.
current through resistor is `i` and voltage across capacitor is `V` then

Options

A. `i_a gt i_b`
B. `V_a = V_b`
C. `V_a lt V_b`
D. `V_a gt V_b`

Answer

D

Explanation

Current through resistor , I = current in the circuit

` = (V_0)/(sqrt(R^2 + X_C^2)) = (V_0)/(sqrt(R^2 + (1//omega C)^2)`
Voltage across capacitor , `V = iX_C`
` = (V_0)/(sqrt(R^2 + (1//omega C)^2) xx (1)/(omega C)) = (V_0)/(sqrt(R^2 omega^2 C^2 + 1))`
As `C_a lt C_b`
` therefore i_a lt i_b` and `V_a gt V_b`