Q 12-03-230JEE MainJEE Main 2020 (8 Jan, Shift 1)Medium
Four resistances of $15\ \Omega$, $12\ \Omega$, $4\ \Omega$ and $10\ \Omega$ respectively, in cyclic order, form a Wheatstone's network. The resistance that is to be connected in parallel with the resistance of $10\ \Omega$ to balance the network is ______ $\Omega$.
Numerical value type. Enter your answer.
Answer: 10
For arms $P, Q, R, S$ in cyclic order, balance requires $PR = QS$ (products of opposite arms equal):
$$15\times4 = 12\times S \Rightarrow S = 5\ \Omega$$
The $10\ \Omega$ arm must be reduced to $5\ \Omega$, which needs another $10\ \Omega$ in parallel.
Solution by Sreeraj P, M.Sc Physics