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. $ np^{2} $
• C. $ n^{2}p $
• D. $ n/p $

Answer 1

Answer: (C)

The resistance of each part $= R/n$
The effective resistance becomes $ R/n^{2} $
Since, the battery voltage is constant
so, $ P\propto \frac{1}{R} $
$ \Rightarrow $ $ \frac{p}{P}=\frac{R}{R/n^{2}} $
$ \Rightarrow $ $ P=n^{2}P $