The resistance of the series combination of two resistances is S. When they are joined in parallel through total resistance is P. If S = nP, then the minimum possible value of n is

Question

The resistance of the series combination of two resistances is S. When they are joined in parallel through total resistance is P. If S = nP, then the minimum possible value of n is (A) 4 (B) 3 (C) 2 (D) 1

Tardigrade Admin · Accepted Answer

Let resistances be R1 and R2 So, S = R1 + R2; P = (R1R2/R1+R2) S = nP R1+R2 = (nR1R2/R1+R2) (R1+R2)2 = nR1R2 If R1 = R2, so minimum value of n = 4.

Q. 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 $n$ is

4

3

2

1

Let resistances be $R_{1}$ and $R_{2}$
So, $S = R_{1} + R_{2}$ ;
$P = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$
$S = n P$
$R_{1} + R_{2} = \frac{n R _{1} R _{2}}{R _{1} + R _{2}}$
$(R_{1} + R_{2})^{2} = n R_{1} R_{2}$
If $R_{1} = R_{2}$ , so minimum value of $n = 4.$

Q. The resistance of the series combination of two resistances is S. When they are joined in parallel through total resistance is P. If S=nP, then the minimum possible value of n is

4

3

2

1

Let resistances be R1​ and R2​ So, S=R1​+R2​; P=R1​+R2​R1​R2​​ S=nP R1​+R2​=R1​+R2​nR1​R2​​ (R1​+R2​)2=nR1​R2​ If R1​=R2​, so minimum value of n=4.

Q. 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 $n$ is

Let resistances be $R_{1}$ and $R_{2}$
So, $S = R_{1} + R_{2}$ ;
$P = \frac{R _{1} R _{2}}{R _{1} + R _{2}}$
$S = n P$
$R_{1} + R_{2} = \frac{n R _{1} R _{2}}{R _{1} + R _{2}}$
$(R_{1} + R_{2})^{2} = n R_{1} R_{2}$
If $R_{1} = R_{2}$ , so minimum value of $n = 4.$