Three resistances of equal values are arranged in four different configurations as shown below. Power…
Three resistances of equal values are arranged in four different configurations as shown below. Power dissipation in the increasing order is
(III) $ < $ (II) $ < $ (IV) $ < $ (I)
(II) $ < $ (III) $ < $ (IV) $ < $ (I)
(I) $ < $ (IV) $ < $ (III) $ < $ (II)
(I) $ < $ (III) $ < $ (II) $ < $ (IV)
Solution
For figure I,
$\begin{aligned} \text { Total resistance } & =3 R \\ \text { I power } & =I^2(3 R)\end{aligned}$
For figure II,
$\begin{aligned} \text { Resistance } & =\frac{2 R}{3} \Omega \\ \text { II power } & =I^2\left(\frac{2 R}{3}\right)\end{aligned}$
For figure III,
$\begin{aligned} \text { Total resistance } & =\frac{R}{3} \Omega \\ \text { III power } & =I^2\left(\frac{R}{3}\right)\end{aligned}$
For figure IV,
Total resistance $\frac{3}{2} \Omega$
IV power $=I^2\left(\frac{3}{2} R\right)$
Hence, option (a) is correct.
