The resistance of two branch parallel circuit is \( 18\,\Omega \). If the resistance of one branch is \( 24\,\Omega \). What is the resistance of other branch?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \( 72\,\Omega \)
For resistors in parallel, the reciprocals of the resistances add.
\( \displaystyle \frac{1}{R_{\mathrm{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \;\Rightarrow\; \frac{1}{R_2} = \frac{1}{18} - \frac{1}{24} \)
\( \displaystyle \frac{1}{R_2} = \frac{4 - 3}{72} = \frac{1}{72} \;\Rightarrow\; R_2 = 72\,\Omega \)
As a check, the parallel combination \( 24 \times 72/(24 + 72) = 18\,\Omega \).