A resistance of 400 Ω and a capacitor of resistance 200 Ω are connected in series to a 220 V, 50 Hz a.c. source. If the current in the circuit is 0.49 ampere find the (i) voltage across the resistor and capacitor (ii) value of inductance required so that voltage and current are in same phase.

Solution

Given,
Resistance, R = 400 Ω
Capacitive reactance,

χ_{C}

= 200 Ω
effective voltage of the source = 200 V
Frequency of the source, f = 50 Hz
Current in the circuit = 0.49 A

(i) The voltage across resistor,

ε_{R} = IR = 0.49 \times 400 = 196 volt .

The voltage across capacitor,

ε_{C} = {IX}_{C} = 0.49 \times 200 = 98 volt .

(ii) For voltage and current to be in same phase

X_{L} = X_{C}

∴

X_{L} = 200 Ω

WL = 200

\Rightarrow

2 πvL = 200

\Rightarrow

L = \frac{200}{2 πv}

= \frac{200}{2 \times 3.14 \times 50} H = \frac{200}{314} H .

which is the required value of inductance.

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