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For the given circuit, what is the voltage across the capacitor?

A series circuit of a capacitor C and a 50 ohm resistor R on a 12 V, 50 Hz supply, with a current I of 0.16 A.

  • A.8.9 V
  • B.18.3 V
  • C.12 V
  • D.19.2 V

Answer: A

The circuit has a capacitor and a 50 ohm resistor in series on a 12 V supply, with a current of 0.16 A. The voltage across the resistor is 0.16 x 50 = 8 V. In a series RC circuit the supply voltage is the square root of the sum of the squares of the two voltages, so

\[ V_{C} = \sqrt{12^{2} - 8^{2}} = \sqrt{80} \]

\[ V_{C} \approx 8.9\ \mathrm{V} \]

So the voltage across the capacitor is 8.9 V, option (A). The values 18.3 V and 19.2 V are larger than the supply, which cannot be, and 12 V would be the supply voltage itself.

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