Question

Two batteries with e.m.f $12V$ and $13V$ are connected in parallel across a load resistor of $10\Omega .$ The internal resistance of the two batteries are $1\Omega$ and $2\Omega$ respectively. The voltage across the load lies between

• A. $11.4V$ and $11.5V$
• B. $11.7V$ and $11.8V$
• C. $11.6V$ and $11.7V$
• D. $11.5V$ and $11.6V$

Answer 1

The correct option is D $11.5V$ and $11.6V$


Equivalent EMF of two cells in parallel,
$E_{eq}=[\frac{E_1}{r_1}+\frac{E_2}{r_2}]r_{eq}$
$E_{eq}=\frac{\frac{12}{1}+\frac{13}{2}}{\frac{1}{1}+\frac{1}{2}}$
$=\frac{\frac{37}{2}}{\frac{3}{2}}=\frac{37}{3}V$
$R_{eq}=\frac{2}{3}$ + 10 $\Omega$
$I=\frac{\frac{37}{3}}{\frac{2}{3}+10}=\frac{37}{3}=\frac{37}{32}A$
Voltage across load = $IR=\left(\frac{37}{32}\right)\left(10\right)=11.56V$