To an AC power supply of 220 V at 50 Hz, a resistor of 20, a capacitor of reactance 25, and an inductor of reactance 45 are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respecti

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Solution

Q.
To an AC power supply of 220 V at 50 Hz, a resistor of 20 $Ω$ , a capacitor of reactance 25 $Ω$ , and an inductor of reactance 45 $Ω$ are connected in series. The corresponding current in the circuit and the phase angle between the current and the voltage is, respectively [2025]

1 15.6 A and $30 °$

2 15.6 A and $45 °$

3 7.8 A and $30 °$

4 7.8 A and $45 °$

Ans.
(4)

Given, $V = 220$ $V, υ = 50$ $Hz$

$R = 20 Ω, X_{L} = 45 Ω, X_{C} = 25 Ω$

Current, $I = \frac{V}{Z} = \frac{220}{\sqrt{R^{2} + {(X_{L} - X_{C})}^{2}}} = \frac{220}{\sqrt{400 + 400}} = \frac{220}{20 \sqrt{2}} = \frac{11}{\sqrt{2}} = 7.8$ $A$

Phase angle, $ϕ = \tan^{- 1} (\frac{X_{L} - X_{C}}{R}) = \tan^{- 1} (\frac{45 - 25}{20}) = \tan^{- 1} (\frac{20}{20})$

$\Rightarrow ϕ = 45 °$

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