Question

All resistors in the circuit have the same resistance, $R$, and the battery is having a constant voltage $V$.

If the equivalent resistance of the circuit is $\frac{10R}{3}$, the amount of current that passes through resistor a is $\frac{xV}{R}$. Find the value of x?

• A. $\frac{1}{20}$
• B. $\frac{1}{10}$
• C. $\frac{3}{10}$
• D. $\frac{10}{9}$
• E. $\frac{10}{3}$

Answer 1

The correct option is C $\frac{3}{10}$

$R_{eq}=\frac{10R}{3}$

The voltage provided by the battery $=V$

Thus current output of the battery $=\frac{V}{\frac{10R}{3}}$$=\frac{3V}{10R}$

The same current passes through resistance $a$.

Thus, $\frac{3V}{10R}=\frac{xV}{R}$

$⟹x=\frac{3}{10}$