Three resistors of resistances 11 $\Omega$, 22 $\Omega$ and 33 $\Omega$ are connected in parallel. Their equivalent resistance is equal to
66 $Omega$
22 $Omega$
12 $Omega$
6 $Omega$
Answer is Wrong!
Answer is Right!
This question was previously asked in
UPSC CDS-1 – 2023
$1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3 + …$
Given resistances are $R_1 = 11 \, \Omega$, $R_2 = 22 \, \Omega$, and $R_3 = 33 \, \Omega$.
$1/R_{eq} = 1/11 + 1/22 + 1/33$
To add these fractions, find a common denominator, which is 66.
$1/R_{eq} = (6 \times 1)/(6 \times 11) + (3 \times 1)/(3 \times 22) + (2 \times 1)/(2 \times 33)$
$1/R_{eq} = 6/66 + 3/66 + 2/66$
$1/R_{eq} = (6 + 3 + 2) / 66 = 11 / 66$
$R_{eq} = 66 / 11 = 6 \, \Omega$.
– The equivalent resistance in a parallel circuit is always less than the smallest individual resistance. In this case, 6 $\Omega$ is less than 11 $\Omega$.