JEE Main · 2004 · 24 Apr 2004 · Offline · Current Electricity

The resistance of the series combination of two resistances is S. When they are joined in parallel through total resistance is

P

. If

S = n P

, then the minimum possible value of

n

Answer: (A)

Solution

For two resistors the series value is

S = R_{1} + R_{2}

and the parallel value is

P = \frac{R _{1} R _{2}}{R _{1} + R _{2}}

. Writing

S = n P

gives

(R_{1} + R_{2})^{2} = n R_{1} R_{2}

, so

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

. This ratio is smallest when the two resistances are equal, where it becomes

\frac{4 R ^{2}}{R ^{2}} = 4

, so the least possible value of

n

is four.

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option