Question

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

• A. $P\sqrt{\frac{R}{Z}}$
• B. $P\left(\frac{R}{Z}\right)$
• C. $P$
• D. $P{\left(\frac{R}{Z}\right)}^2$

Answer 1

Answer: (D)

AC source Impedance =Z
$P^{\prime }=V.I\cdot \cos \varphi$
$P=\frac{V^2}{R}$
$P^{\prime }=V\cdot \left[\frac{V}{Z}\right]\cdot \cos \varphi$
$\Rightarrow V^2=PR$
$P^{\prime }=\frac{V^2}{Z}\cdot \frac{R}{Z}$ (From phasor diagram)
$P^{\prime }=\frac{(PR)R}{Z^2}$
$P^{\prime }={\left(\frac{R}{Z}\right)}^{2}P$