Question

The incorrect option in the given circuit if the reading of ammeter is zero is

• A. The value of ${\epsilon }_1$ will be $\frac{\epsilon (R+r)}{R}$
• B. Current in $R$ is $\frac{{\epsilon }_1}{r+R}$
• C. Value of ${\epsilon }_1$ will be $\epsilon$
• D. Potential across $2R$ is zero.

Answer 1

The correct option is C Value of ${\epsilon }_1$ will be $\epsilon$


$\because$ Reading in Ammeter is zero, so the current $\left(i\right)$ will only flow in the upper circuit.
Where $i=\frac{{\epsilon }_1}{R+r}=i_r=i_R$
Here ,$V_S-V_R=V_Q-V_P=V_M-V_N=\epsilon$
Also $V_S-V_R={\epsilon }_1-r{i}_r={\epsilon }_1-r.\frac{{\epsilon }_1}{R+r}=\frac{{\epsilon }_{1}R}{R+r}=\epsilon$
$\therefore {\epsilon }_1=\frac{\epsilon (R+r)}{R}$
$\therefore$ (a) is correct and (c) is incorrect.
$\because$ no current is flowing through $2R$
$\therefore$ potential difference across $2R=0$
$\therefore$ (d) is also correct.