Alternating Current Ques 10
10. 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
[2015]
(a) $P \sqrt{\frac{R}{Z}}$
(b) $P(\frac{R}{Z})$
(c) $P$
(d) $P(\frac{R}{Z})^{2}$
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Answer:
Correct Answer: 10.(d)
Solution:
- (d) Pure resistor $L-R$ series circuit
Phasor diagram
For pure resistor circuit, power
$ P=\frac{V^{2}}{R} \Rightarrow V^{2}=PR $
For $L-R$ series circuit, power
$ P^{1}=\frac{V^{2}}{Z} \cos \theta=\frac{V^{2}}{Z} \cdot \frac{R}{Z}=\frac{PR}{Z^{2}} \cdot R=P(\frac{R}{Z})^{2} $
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