Question

Consider the following statements regarding the network shown in the figure.

(1) The equivalent resistance of the network between points $A$ and $B$ is independent of the value of $G$.
(2) The equivalent resistance of the network between points $A$ and $B$ is $\frac{4}{3}R$.
(3) The current through $G$ is zero.
Which of the above statement(s) is/are true?

• A. (2) and (3)
• B. (2) alone
• C. (1), (2) and (3)
• D. (1) alone

Answer 1

The correct option is C (1), (2) and (3)

Wheatstone bridge is balanced and hence current through $G$ is zero
Effective resistance is independent of $G$ in this case.
$R_{eff}=\frac{(P+Q)(R+S)}{(P+Q+R+S)}$
$R_{eff}=\frac{4}{3}R$