Question

Three resistors of values 2 Ω, 4 Ω, 6 Ω are connected in parallel. The equivalent resistance of combination of resistors is _____________.

• A. 12 Ω
• B. $\frac{11}{12}$ Ω
• C. $\frac{1}{12}$ Ω
• D. $\frac{12}{11}$ Ω

Answer 1

The correct option is D $\frac{12}{11}$ Ω

Let,
$R_1$ = 2 Ω. $R_2$ = 4 Ω, $R_3$ = 6 Ω

For resistance connected in parallel combination, the equivalent resistance will be:
$\frac{1}{R_{eq}}$ = $\frac{1}{R_1}$+$\frac{1}{R_2}$ + $\frac{1}{R_3}$
$\frac{1}{R_{eq}}$ = $\frac{1}{2}$+$\frac{1}{4}$ + $\frac{1}{6}$
$\frac{1}{R_{eq}}$ = $\frac{11}{12}$
$R_{eq}$ = $\frac{12}{11}$ Ω