Question 3.39: An inductive coil has a resistance of 2.5 Ω and an inductive......
An inductive coil has a resistance of 2.5 Ω and an inductive reactance of 25 Ω. This coil is connected in series with a variable capacitance and a voltage of 200 V at 50 Hz is applied across the series circuit. Calculate the value of C at which the current in the circuit will be maximum. Also calculate the power factor, impedance, and current in the circuit under that condition.
When current is maximum in an R, L, C series circuit, the circuit is under the resonance condition. At resonance, X_L = X_C and Z = R.
Here
\begin{aligned} & \mathrm{X}_{\mathrm{L}}=25 \Omega \text { (given), } \mathrm{f}_0=50 \mathrm{~Hz} \\ & \mathrm{X}_{\mathrm{C}}=\frac{1}{2 \pi \mathrm{f}_0 \mathrm{C}}=\mathrm{X}_{\mathrm{L}}=25 \Omega \end{aligned}or, \mathrm{C}=\frac{1}{2 \pi \mathrm{f}_0 \times 25}=\frac{1}{6.28 \times 50 \times 25}=127.4 \times 10^{-6} \mathrm{~F}
At resonance, X_L=X_C, Z=R. The circuit behaves like a resistive circuit. Therefore, the power factor = 1. Impedance, Z = R, and current is maximum.
\mathrm{I}_{\mathrm{m}}=\frac{\mathrm{V}}{\mathrm{R}}=\frac{200}{2.5}=80 \mathrm{~A}