Question

In an electric circuit, two identical resistors are arranged in parallel. Assuming the voltage is kept constant, what is the ratio between the new current and the old current when a third identical resistor is added in parallel with the earlier two?

• A. $\frac{4}{9}$
• B. $\frac{2}{3}$
• C. $1$
• D. $\frac{3}{2}$
• E. $\frac{9}{4}$

Answer 1

The correct option is D $\frac{3}{2}$

Let the resistance of each resistor be $R$ and voltage be $V$.

Parallel combination of 2 resistors : Equivalent resistance $\frac{1}{r_{eq}}=\frac{1}{R}+\frac{1}{R}$ $⟹r_{eq}=\frac{R}{2}$

Thus current in the circuit $I=\frac{V}{r_{eq}}=\frac{2V}{R}$

Parallel combination of 3 resistors : New equivalent resistance $\frac{1}{r_{eq}^{\prime }}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$

$⟹r_{eq}^{\prime }=\frac{R}{3}$

Thus new current in the circuit $I^{\prime }=\frac{V}{r_{eq}^{\prime }}=\frac{3V}{R}$

$\therefore$ $\frac{I^{\prime }}{I}=\frac{3V/R}{2V/R}=\frac{3}{2}$