Q. Two identical cells weather connected in parallel or in series gives the same current when connected to an external resistance 1.5$\ \Omega$. Find the value of internal resistance of each cell.
A) 1$\ \Omega$
B) 0.5$\ \Omega$
C) Zero
D) 1.5$\ \Omega$
Explanation
(d) Let $n$ cells be in series and $m$ in parallel, then
$\frac{nE}{R + nr} = \frac{E}{R + \frac{r}{m}}$
$\Longrightarrow \ \ \ n\left\lbrack R + \frac{r}{m} \right\rbrack = R + nr$
$\Longrightarrow nRm + nr = Rm + mnr$
$\Longrightarrow 6 + 2r = 3 + 4r$
$\Longrightarrow 2r = 3$
$\Longrightarrow \ \ r = 1.5\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.