Question

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

• A. $R$
• B. $\frac{R}{2}$
• C. $\frac{R}{4}$
• D. $\frac{R}{6}$

Answer 1

The correct option is A $R$

The connection of wires is as shown below.
We have to calculate equivalent resistance across the opposite corners i.e. across A and D or B and C. If we take two corners B and C, then we can clearly see that the resistances of AB and AC, and CD and BD are in series.
So the equivalent resistance across CAB is $2R$ ( CA and AB are in series) and CDB is also $2R$ ( CD and BD are in series).

The two equivalent resistances across CAB and CDB are in parallel. Hence, the equivalent resistance across the two corners i.e. B and C is $\frac{1}{R_{eq}}=\frac{1}{2R}+\frac{1}{2R}$.
On solving we get, $R_{eq}=R$. Similarly, equivalent resistance across A and D will also be $R$.

Hence the equivalent resistance across the opposite corners is $R$.