Question

Four resistances are connected to a DC battery as shown in figure. Maximum power will be developed across___ ohm resistance.

• A. 3
• B. 6
• C. 12
• D. 36

Answer 1

The correct option is C

12

Among $3\Omega$ and $6\Omega$, more power is developed across $3\Omega$ (\because $P\propto \frac{1}{R}$, as they are in parallel). Similarly among $12\Omega$ and $36\Omega$ more power is developed across $12\Omega$ resistance. Now, suppose i is the main current. Then it is distributed in inverse ratio of resistances as shown in figure.
From $P=i^{2}R$
$P_3{\left(\frac{2i}{3}\right)}^2\left(3\right)=\frac{4}{3}{i}^2{P}_{12}{\left(\frac{3i}{4}\right)}^2\left(12\right)=\frac{27}{4}{i}^{2}or{P}_{12}>P_3$