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,

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

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

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

  • Then since they are orthogonal to each other,

"\\qquad\\qquad\n\\begin{aligned}\n\\small \\sqrt{V_b^2 +V_c^2 }&=\\small 220\\\\\n\\small V_c&=\\small \\sqrt{220^2 -100^2}=195.96V\n\\end{aligned}"

  • Then, by the equation for a capacitor

"\\qquad\\qquad\n\\begin{aligned}\n\\small V_c &=\\small IX_c=\\frac{I}{2\\pi f C}\\\\\n\\small C&=\\small \\frac{I}{2\\pi f V_c}\\\\\n&=\\small \\frac{5A}{2\\pi\\times 50Hz\\times 195.96V}\\\\\n&=\\small \\bold{81.22\\,\\mu F}\n\\end{aligned}"



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