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) $R _{ eq }=\frac{R \times R}{R+R}=\frac{R}{2}$
$\Rightarrow P_{1}=\frac{E^{2}}{\frac{R}{2}}=\frac{2 E^{2}}{R}$
In choice (b)
$R _{\text {eq }}=R+R=2 R$
$P_{2}=\frac{E^{2}}{2 R}=\frac{0.5 E^{2}}{R}$
In choice (c)
$R _{ eq }=\frac{R}{2}+R=\frac{3 R}{2}$
$P_{3}=\frac{2 E^{2}}{3 R}=\frac{0.6 E^{2}}{R}$
In choice (d)
$R _{ eq }=\frac{2 R \times R}{2 R+R}=\frac{2 R}{3}$
$P_{4}=\frac{3 E^{3}}{2 R}=\frac{1.5 E^{2}}{R}$
So, $P_{1}$ is maximum.