Question

If a third identical resistor is added in parallel in a circuit of two identical parallel resistors. Calculate the ratio of the new equivalent resistance to the old?

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

Answer 1

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

Let the resistance of each resistor be $R$.

Equivalent resistance of two resistors in parallel, $\frac{1}{R_{eq}}=\frac{1}{R}+\frac{1}{R}$

$⟹R_{eq}=\frac{R}{2}$

Equivalent resistance of three resstors in parallel, $\frac{1}{R_{eq}^{\prime }}=\frac{1}{R}+\frac{1}{R}+\frac{1}{R}$

$⟹R_{eq}^{\prime }=\frac{R}{3}$

$\therefore \frac{R_{eq}^{\prime }}{R_{eq}}=\frac{R/3}{R/2}=\frac{2}{3}$