Question

A $10 \, \text{V}$ battery with internal resistance $\text{1} \, \Omega $ and a $15 \, \text{V}$ battery with internal resistance $0.6\Omega$ are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to:

• A. $11.9 \, V$
• B. $13.1 \, V$
• C. $12.5 \, V$
• D. $24.5 \, V$

Answer 1

Answer: (B)

The equivalent emf of the battery parallel combination is given as
Equation $= \, \frac{\frac{E_{1}}{r_{1} \, \, } + \, \frac{E_{2}}{r_{2}}}{\frac{1}{r_{1}} \, + \, \frac{1}{r_{2}}}$
$= \, \frac{\frac{10}{1} \, + \, \frac{15}{0.6}}{\frac{1 \, }{1} \, + \, \frac{1}{ \, 0.6}}= \, \frac{10 + \, \frac{150}{6}}{1 + \, \frac{10}{6}} \, $
$=\frac{105}{8}$
$=13.1 \, V$
$\therefore \, \, \, $ The reading measured by voltmeter $=13.1 \, V$