Question

A resistance 'R' draws power 'P' when connected to an AC source. If an inductance is now placed in series with the resistance such that the impedance of the circuit becomes 'Z' the power drawn will be

$straight P open parentheses straight R over straight Z close parentheses squared$
$straight P square root of straight R over straight Z end root$
$straight P open parentheses straight R over straight Z close parentheses$

P

Solution

straight P open parentheses straight R over straight Z close parentheses squared

when a resistor is connected to an AC source. The power drawn will be
P=V_rms.I_{rms
$straight V subscript rms space. straight V subscript rms over straight R rightwards double arrow space straight V subscript rms superscript 2 space equals space PR When space an space inductor space is space connected space in space series space with space the space resistor comma space then space the space power drawn space will space be straight P apostrophe space equals straight V subscript rms. straight I subscript rms cosϕ where space straight ϕ space equals space phase space difference therefore space straight P apostrophe space equals space fraction numerator straight V subscript rms superscript 2 over denominator straight R end fraction. space straight R squared over straight Z squared space equals space straight P. straight R. straight R over straight Z squared rightwards double arrow space straight P apostrophe space equals space fraction numerator straight P. straight R squared over denominator straight Z squared end fraction space equals space straight P open parentheses straight R over straight Z close parentheses squared$}

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