Question

A set of n identical resistors, each of resistance R ohm, when connected in series have an effective resistance of X ohm and when the resistors are connected in parallel, the effective resistance is Y ohm. Find the relation between R, X and Y.

• A. $X^2=RY$
• B. $Y^2=XR$
• C. $R^2=XY$
• D. $R=X/Y$

Answer 1

Answer: (C)

$R^2=XY$

We know that if n equal resistors are connected in series equivalent resistance is given by

$X=nR$

And,if n equal resistors are connected in parallel, equivalent resistance is given by

$Y=\frac{R}{n}$

Now,$XY=nR\times \frac{R}{n}=R^2$

$⟹R^2=XY$

Answer-(C)