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  • To an ac power supply of 220 V at 50 Hz , a resistor of $20 \Omega$, a capacitor of reactance $25 \Omega$ and an inductor of reactance $45 \Omega$ are connected in series.

Q.11) To an ac power supply of 220 V at 50 Hz , a resistor of $20 \Omega$, a capacitor of reactance $25 \Omega$ and an inductor of reactance $45 \Omega$ are connected in series. The corresponding current in the circuit and the phase angle between the current and the volage is, respectively -

A) $15.6 A$ and $45{ }^{\circ}$

B) $7.8 A$ and $30^{\circ}$

C) $7.8 A $ and $45^{\circ}$

D) $15.6 A$ and $30^{\circ}$

Answers (1)

best_answer


Solution:
Given:
Voltage $V=220 \mathrm{~V}$
Resistance $R=20 \Omega$
Capacitive reactance $X_C=25 \Omega$
Inductive reactance $X_L=45 \Omega$

Net reactance: $X=X_L-X_C=45-25=20 \Omega$
Impedance: $Z=\sqrt{R^2+X^2}=\sqrt{20^2+20^2}=\sqrt{800}=20 \sqrt{2} \Omega$
Current:

$$
I=\frac{V}{Z}=\frac{220}{20 \sqrt{2}}=\frac{11}{\sqrt{2}} \approx 7.8 \mathrm{~A}
$$
Phase angle:

$$
\tan \phi=\frac{X}{R}=\frac{20}{20}=1 \Rightarrow \phi=45^{\circ}
$$
Hence, the answer is option (3) $7.8 A$ and $45^{\circ}$.

 

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Dimpy

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