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 :

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)  np2  (C)  n2p  (D)  n/p

Tardigrade Admin · Accepted Answer

The resistance of each part = R/n The effective resistance becomes R/n2 Since, the battery voltage is constant so, P propto (1/R) ⇒ (p/P)=(R/R/n2) ⇒ P=n2P

Q. 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 :

$n p$

$n p^{2}$

$n^{2} p$

$n / p$

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

Q. 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 :

np

np2

n2p

n/p