Question

The circuit given below consists of cells with their internal resistance

$\left(ii\right)$ The equivalent internal resistance of the combination is

• A. $\frac{24}{13}\Omega$
• B. $\frac{13}{24}\Omega$
• C. $\frac{25}{13}\Omega$
• D. $\frac{13}{12}\Omega$

Answer 1

The correct option is C $\frac{25}{13}\Omega$

As three cells are in parallel, their effective internal resistance is
$\frac{1}{r_{123}}=\frac{1}{r_1}+\frac{1}{r_2}+\frac{1}{r_3}$
$=\frac{1}{2}+\frac{1}{3}+\frac{1}{4}$
$=\frac{6+4+3}{12}=\frac{13}{12}$
$r_{123}=\frac{12}{13}$

Now $1\text{V}$ is in series to the parallel combination, hence net resistance of combination is
$R_{eff}=r_4+r_{123}$
$=1+\frac{12}{13}$
$=\frac{25}{13}\Omega$