JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Current Electricity

In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be

\frac{x}{2}

. The value of

x

is ______.

Answer: 3

Solution

The equivalent resistance is:

R = \frac{ma}{3} + \frac{a}{2 m}

For minimum resistance, differentiate with respect to m and set equal to zero:

\frac{d R}{d m} = \frac{a}{3} - \frac{a}{2 m ^{2}} = 0

Solving:

\frac{a}{3} = \frac{a}{2 m ^{2}}

2 m^{2} = 3

m^{2} = \frac{3}{2}

m = \frac{3}{2}

Comparing with

m = \frac{x}{2}

, we get

x = 3

JEE Main · 2022 · 27 Jun 2022 · Shift 2 · Integer answer