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, f_{0 }= 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