A resistor of resistance 400 ohm and a capacitor of reactance 200 ohm are connected in series of a 200 V, 50 Hz source. If the current in the circuit is 0.49 A, find the voltage across the resistor and capacitor. What is the value of inductance required so that voltage and current are in phase ?

Explanation

Given `R= 400 Omega X_(C) = 200 Omega`
`epsilon_("rms") = 220 V f, = 50 Hz `
`I_("rms") = 0.49 A `
(i) Voltage across the resistor is
`V_(R) = I_("rms") xxR = 0.49 xx400 = 196 V `
Voltage across the capacitor is
`V_(C) = I_("rms") xxX_(C) = 0.49 xx200 = 98 V `
(ii) Voltage and current are in phase only when the circuit is at resonance . If `X_(L)` is the reactance of the inductor then
`X_(c) = X_(L)`
`implies 2pifL= X_(C)`
`implies L = (X_(C))/(2pif) = (200)/(2xxpixx50) = 0.63 H `