Answer to Question #200534 in Electric Circuits for Shani

Question #200534

A series R-L circuit is connected to 110V ac source.If voltage across resistor is 85V ,find power dissipated in circuit


1
Expert's answer
2021-05-31T15:15:46-0400

Since the voltages across the inductor and the resistor are 90° out of phase, we obtain the voltage across the inductor in the phase domain as follows: If the voltage across the resistor is V1

The voltage across the inductor will be jV2


. Assume the voltage of the source is V3

Applying kvL law


V1+jV2=V1cos(wt)+V2sin(wt)=V3cos(wtθ)=85+V2sin(wt)=110cos(wtθ)V_1+jV_2=V_1cos(wt)+V_2sin(wt)=V_3cos(wt-\theta)=85+V_2sin(wt)=110cos(wt-\theta)

110=852+V22110=\sqrt{85^2+V_2^2}

V2=69.82VV_2=69.82V

For example

Pave=12VR2RP_{ave}=\frac{1}{2}\frac{V_R^2}{R}

Assume

R=20ohmR=20 ohm

And VR=85 V

Put value

Pav=1285220=180.6WP_{av}=\frac{1}{2}\frac{85^2}{20}=180.6 W


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