Determine Capacitance of capacitor:

A 20 Ω resistor is connected in series with a coil, a capacitor and an ammeter across a 25 V variable frequency supply. While the frequency is 400 Hz, the current is at its maximum value of 0.5 A and potential difference across the capacitor is 150 V. Determine:

1. Capacitance of capacitor, and

2. Resistance and inductance of coil.

Figure

Solution

 (a) Let capacitance = C farad

Resonant frequency, f₀ = 400 Hz

Capacitive reactance, X _C =1 / ωC =   1 / (2π × 400 × C) = (1/800π × C) Ω

Voltage across capacity = I_m X_C = 150 V

                                         I_m = 0.5 A

∴          0.5 / 800π C = 150

    C =   0.5 / (800 ×π × 150)

= 1.3263 × 10^{- 6} F

or         C = 1.3263 μF

 (b)       Let, R_L and L be the resistance and inductance of coil respectively

Current, I _m      =          V/ (R + R_L)

                    0.5 = 25 / 20 + R_L (?Applied voltage V = 25 V)

                        R_L = 30 Ω