JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Current Electricity

The equivalent resistance of series combination of two resistors is '

s

'. When they are connected in parallel, the equivalent resistance is '

p

'. If

s = n p

, then the minimum value for

n

is ______ (Round off to the Nearest Integer)

Answer: 4

Solution

For two resistances

R_{1}

and

R_{2}

s = R_{1} + R_{2}, p = \frac{R _{1} R _{2}}{R _{1} + R _{2}}

n = \frac{s}{p} = \frac{( R _{1} + R _{2} ) ^{2}}{R _{1} R _{2}}

Writing

(R_{1} + R_{2})^{2} = (R_{1} - R_{2})^{2} + 4 R_{1} R_{2}

gives

n = 4 + \frac{( R _{1} - R _{2} ) ^{2}}{R _{1} R _{2}} \geq 4

with equality only when

R_{1} = R_{2}

. The minimum value of

n

4

JEE Main · 2021 · 17 Mar 2021 · Shift 1 · Integer answer