Question

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

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

Answer 1

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

$$\begin{array}{c}Accordingtoquestion.....................\\ Theresis\tan ceofeachpart=\frac{R}{n}\\ and,theeffectiveresistancebecome=\frac{R}{n^2}\\ so,thebetteryvoltageisconstant:\\ \Rightarrow \frac{P^{{}^{\prime }}}{P}=\frac{R}{\frac{R}{n^2}}\\ \Rightarrow P^{{}^{\prime }}=n^{2}P\\ thereforthecorrectoptionisC.\end{array}$$