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Question 4.11: A 2 μF capacitor is connected in series with a 100 F resisto......

A 2 μF capacitor is connected in series with a 100 F resistor across a 115 V 400 Hz a.c. supply. Determine the impedance of the circuit and the current taken from the supply.

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First we must find the reactance of the capacitor, X_C:

X_{c}={\frac{1}{2\pi fC}}={\frac{1}{6.28 \times 400\times2\times 10^{-6}}}={\frac{10^{6}}{5,024}}=199{\Omega}

Now we can find the impedance of the C–R series circuit:

\scriptstyle Z={\sqrt{R^{2}+X^{2}}}={\sqrt{199^2}}+100^{2}={\sqrt{49,601}}=223~\Omega

The current taken from the supply can now be found:

I_{S}={\frac{V_{S}}{Z}}={\frac{115}{223}}=0.52{\mathrm{A}}

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