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Properties of Conjugate of a Complex Number

In a given R-...

Question

In a given R-C circuit, power consumed in the circuit is [in watts]

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Solution

$Z = \sqrt{R^{2} + X_{L}^{2}} = \sqrt{2^{2} + 4^{2}} = 2 \sqrt{5}$
$i = \frac{ϵ}{Z} = \frac{10}{2 \sqrt{5}} = \sqrt{5} \Rightarrow P = i^{2} R = (\sqrt{5})^{2} \times 2 = 10 watt$

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