Question

Six cells, each of emf $5V$ and internal resistance $0.1\Omega$ are connected as shown in Figure. The reading of the ideal voltmeter $V$ is

• A. $30$ V
• B. $5$ V
• C. $15$ V
• D. zero
• E. $0.5V$

Answer 1

Answer: (D)

$E_{\text{eff }}=\frac{E_1{r}_2-E_2{r}_1}{r_1+r_2}$
$=\frac{E(5r)-E(r)}{6r}$
$=\frac{2}{3}E$
As $E=5V$
$E_{\text{eff }}=\frac{2}{3}\times 5=\frac{10}{3}V$
Reading of voltmeter $=$ Terminal potential of cell $6$
$v=5-0.1i$
But $i=\frac{E_{\text{eff }}}{R_{\text{eff }}}=\frac{10}{0.4}=\frac{100}{4}=25A$
$\therefore V=5-0.1t$
$=5-2.5=2-1N$