Two impedances \( Z_{1} \) and \( Z_{2} \) when connected separately across a \( 230 \mathrm{~V}...

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Two impedances \( Z_{1} \) and \( Z_{2} \) when connected separately across a \( 230 \mathrm{~V}, 50 \mathrm{~Hz} \) supply consume \( 100 \mathrm{~W} \) and \( 60 \mathrm{~W} \) at power factor of \( 0.5 \) lagging and \( 0.6 \) leading respectively. If these impedances are now connected in series across the same supply, find
(a) total power absorbed and overall power factor
(b) the value of reactance to be added in series so as to raise the overall power factor to unity.
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