Question

A resistor R has power dissipation P with cell voltage E. The resistor is cut in n equal parts and all parts are connected in parallel with same cell. The new power dissipation is:

• A. nP
• B. $n{P}^2$
• C. $n^{2}P$
• D. $\frac{n}{P}$

Answer 1

The correct option is C $n^{2}P$

Resistance of each part $=\frac{R}{n}$
Effective resistance $=\frac{R}{n^2}$
Battery voltage is constant
$P\propto \frac{1}{R}\Rightarrow \frac{P^{\prime }}{P}=\frac{P}{R/n^2}=n^2$