Question

Four wires each of same length, diameter and material are connected to each other to form a square. If the resistance of each wire is R, then equivalent resistance across the opposite corners is:

• A. R
• B. R/2
• C. R/4
• D. none of the above

Answer 1

The correct option is A

R

Suppose the formed square is ABCD.

Since the resistance have to be calculated accross the opposite corners, let us calculate resistance between A and C.

We can observe that AB and BC are in series and similarly AD and DC are in series, which gives,

$AB+BC=AD+DC=R+R=2R$

Now, we have two wires of resistance $2R$ connected in parallel.

Hence, $\frac{1}{R_{eq}}=\frac{1}{2R}+\frac{1}{2R}$

So, $R_{eq}=R$