Question

In the circuit shown in figure, reading of ammeter will

i) increases if only $S_1$ is closed.
ii) decreases if only $S_1$ is closed.
iii) increases if $S_1$ and $S_2$ are both closed.
iv) decreases if $S_1$ and $S_2$ are both closed.

Which of the above statements is/are correct:

• A. (i) and (iii)
• B. (i) and (iv)
• C. (ii) and (iii)
• D. (ii) and (iv)

Answer 1

The correct option is A (i) and (iii)

When both $S_1$ and $S_2$ are open:
$I=\frac{E}{R+r}$.

When $S_1$ is closed:

$I_1=\frac{E}{\frac{R}{2}+r}>I$

$\Rightarrow$ (i) is correct.

When both switches are closed:
Effective EMF:
$E^{\prime }=\frac{\frac{E}{r}+\frac{E}{r}}{\frac{1}{r}+\frac{1}{r}}=E$

Effective resistance in cell:
$r^{\prime }$ = $\frac{r}{2}$.
Hence,
$I_2=\frac{E}{\frac{R}{2}+\frac{r}{2}}$

$I_2=\frac{2E}{R+r}>I$

$\Rightarrow$ (iii) is correct.