Question

Two batteries, one of emf $18\text{volts}$ and internal resistance $2\Omega$ and the other of emf $12\text{volts}$ and internal resistance $1\Omega$, are connected as shown. The reading of the voltmeter $V$ will be:

• A. $18\text{volts}$
• B. $30\text{volts}$
• C. $14\text{volts}$
• D. $15\text{volts}$

Answer 1

The correct option is C $14\text{volts}$

We can redraw the circuit as shown below.

So. the voltmeter will record the magnitude of net emf of the combination of the two cells i.e. $E_{eq}$ across points $\text{A}$ and $\text{B}$.

Now, for parallel combination of cells,

$E_{eq}=\frac{\sum \left(\frac{E}{r}\right)}{\sum \left(\frac{1}{r}\right)}=\frac{\frac{18}{2}+\frac{12}{1}}{\frac{1}{2}+1}=\frac{9+12}{\frac{3}{2}}$

$\therefore E_{eq}=14\text{volts}$

So the voltmeter will read $14\text{volts}$.