Answer to Question #188645 in Electric Circuits for Miles Montego

Question #188645

A tungsten filament bulb rated at 500w, 100v is to be connected in series to a capacitor across 220v, 50hz supply. Calculate the capacitor such that the voltage and power consumed by the bulb are according to the rating of the bulb


1
Expert's answer
2021-05-06T19:15:15-0400

Explanations & Calculations


  • This symbolizes an RC circuit.


  • The current flowing in the circuit can be found by the bulb assuming it is a resistor,

I=PV=500W100V=5A\qquad\qquad \begin{aligned} \small I&=\small \frac{P}{V}=\frac{500W}{100V}=5A \end{aligned}

  • If the voltage across the cap is Vc\small V_c, then the phasor sum of the voltages will be

Vb+Vc=220V\qquad\qquad \begin{aligned} \small \vec{V_b}+\vec{V_c}&=\small 220V \end{aligned}

  • Then since they are orthogonal to each other,

Vb2+Vc2=220Vc=22021002=195.96V\qquad\qquad \begin{aligned} \small \sqrt{V_b^2 +V_c^2 }&=\small 220\\ \small V_c&=\small \sqrt{220^2 -100^2}=195.96V \end{aligned}

  • Then, by the equation for a capacitor

Vc=IXc=I2πfCC=I2πfVc=5A2π×50Hz×195.96V=81.22μF\qquad\qquad \begin{aligned} \small V_c &=\small IX_c=\frac{I}{2\pi f C}\\ \small C&=\small \frac{I}{2\pi f V_c}\\ &=\small \frac{5A}{2\pi\times 50Hz\times 195.96V}\\ &=\small \bold{81.22\,\mu F} \end{aligned}



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