Question

Consider four circuits shown in the figure below. In which circuit power dissipated is greatest? (Neglect the internal resistance of the power supply)

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Let each resistance is $R$
$P=\frac{E^2}{R_{\text{eq }}}$
In choice (a) $R_{eq}=\frac{R\times R}{R+R}=\frac{R}{2}$
$\Rightarrow P_1=\frac{E^2}{\frac{R}{2}}=\frac{2E^2}{R}$
In choice (b)
$R_{\text{eq }}=R+R=2R$
$P_2=\frac{E^2}{2R}=\frac{0.5E^2}{R}$
In choice (c)
$R_{eq}=\frac{R}{2}+R=\frac{3R}{2}$
$P_3=\frac{2E^2}{3R}=\frac{0.6E^2}{R}$
In choice (d)
$R_{eq}=\frac{2R\times R}{2R+R}=\frac{2R}{3}$
$P_4=\frac{3E^3}{2R}=\frac{1.5E^2}{R}$
So, $P_1$ is maximum.