Question

Power dissipated in an L-C-R series circuit connected to an AC source of emf is

$fraction numerator straight epsilon squared straight R over denominator open square brackets straight R squared space plus space open parentheses space Lω space minus begin display style 1 over Cω end style close parentheses squared close square brackets end fraction$
$fraction numerator straight epsilon squared space square root of straight R squared space plus space open parentheses Lω space minus space 1 over Cω close parentheses squared end root over denominator straight R end fraction$
$fraction numerator straight epsilon squared space open square brackets straight R squared space plus space open parentheses Lω space minus space begin display style 1 over Cω end style close parentheses squared close square brackets over denominator straight R end fraction$
$fraction numerator straight epsilon squared straight R over denominator square root of straight R squared space plus open parentheses Lω minus begin display style 1 over Cω end style close parentheses squared end root end fraction$

Solution

fraction numerator straight epsilon squared straight R over denominator open square brackets straight R squared space plus space open parentheses space Lω space minus begin display style 1 over Cω end style close parentheses squared close square brackets end fraction

space P space equals space I squared subscript r m s end subscript space R space equals space fraction numerator epsilon subscript r m s end subscript superscript 2 R over denominator vertical line Z vertical line squared end fraction space equals space fraction numerator straight epsilon squared straight R over denominator open square brackets straight R squared space plus space open parentheses ωL space minus begin display style 1 over ωC end style close parentheses squared close square brackets end fraction

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