Question

Two identical cells connected in series send $1.0A$ current through a $5\Omega$ resistor. When they are connected in parallel, they send $0.8A$ current through the same resistor. What is the internal resistance of the cell?

• A. $0.5\Omega$
• B. $1.0\Omega$
• C. $1.5\Omega$
• D. $2.5\Omega$

Answer 1

The correct option is D $2.5\Omega$

Let emf of each cell $=E$ and internal resistance $=r$.
For series: $E+E=1(r+r+5)$ (using $V=IR$)
or $2E=2r+5....\left(1\right)$
For parallel: $E=0.8R_{eq}=8(r||r+5)=0.8(\frac{rr}{r+r}+5)=0.8(r/2+5)$
$E=0.4r+4....\left(2\right)$
From (1) and (2), $0.8r+8=2r+5\Rightarrow r=\frac{3}{1.2}=5/2=2.5\Omega$