Question

In the given circuit, the potential difference across the capacitor is $10\text{V}$. Each resistance is $3\Omega$. The cell is ideal. The emf of the cell is

• A. $14\text{V}$
• B. $16\text{V}$
• C. $18\text{V}$
• D. $24\text{V}$

Answer 1

The correct option is A $14\text{V}$

$V_a=\frac{i}{4}R+iR+V_b$

$\Rightarrow V_a-V_b=\frac{5}{4}iR=10...\left(1\right)$

$R_{net}=R+\frac{\left(3R\right)\left(R\right)}{(3R+R)}$

$\Rightarrow R_{net}=\frac{7}{4}R$

$\Rightarrow i=\frac{E}{R_{net}}$

$\Rightarrow i=\frac{E}{\left(\frac{7}{4}\right)R}=\left(\frac{4E}{7R}\right)$

Substituting in Equation $\left(1\right)$, we get

$\left(\frac{5}{4}\right)\left(\frac{4E}{7R}\right)\times R=10$

$\Rightarrow E=14\text{V}$

Hence, the correct answer is (A).