JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Current Electricity

Four resistances of

15Ω, 12Ω, 4Ω

and

10Ω

respectively in cyclic order to form Whetstone's network. The resistance that is to be connected in parallel with the resistance of

10Ω

to balance the network is ____ .

Answer: 10

Solution

For a balanced Wheatstone bridge the ratios of the arms are equal, which here fixes the parallel section, the

10 Ω

resistor together with the unknown

R

, at an equivalent resistance of

R_{e q} = 5 Ω

. Writing

\frac{1}{R _{e q}} = \frac{1}{10} + \frac{1}{R}

then gives

\frac{1}{5} = \frac{1}{10} + \frac{1}{R}

, so

\frac{1}{R} = \frac{1}{10}

and the unknown resistance is

R = 10 Ω

JEE Main · 2020 · 08 Jan 2020 · Shift 1 · Integer answer