Question

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

(i) When capacitor is air filled.

(ii) When capacitor is mica filled.

Current through resistor is i and voltage across capacitor is V then:

Options

• V_a = V_b

• V_a < V_b

• V_a > V_b

• i_a > i_b

Answer 1

V_a > V_b

Explanation:

`"x"_"c" = 1/(2pi"fC")`

current in ciruit

`"I" = "V"/"Z" = "V"/sqrt ("R"^2 + (1/(2pi"fC"))^2`

`"Or I" = (2pi"fC")/sqrt (4pi^2"f"^2"C"^2 +1) xx "V"`

Voltage drop across capacitor

`"V"_"c" = "I" xx "X"_"c" = (2pi"fC")/sqrt (4pi^2"f"^2"C"^2 +1)  xx 1/(2pi"fC")`

`"V"_"c" = "V"/sqrt (4pi^2 "f"^2 "C"^2 "R"^2 + 1)`

When mica is introduced capacitance will increase, hence voltage across capacitor gets decreased.