Match equivalent resistance of the following circuits between A and B.
List-I
List-II
(I)
(P) $\frac{R}{3}$
(II)
(Q) R
(III)
(R) $\frac{2 R}{5}$
(IV)
(S) $\frac{4 R}{3}$

(T) $\frac{R}{2}$

Question

Match equivalent resistance of the following circuits between A and B. List-I List-II (I) (P) 3 R ​ (II) (Q) R (III) (R) 5 2 R ​ (IV) (S) 3 4 R ​ (T) 2 R ​

TestHub · Accepted Answer

(I) Balanced bridge: X, Y and Z are at the same potential, so the diagonal resistors carry no current; the network reduces to give $R_{A B} = R$ → I → Q.

(II) Ladder network between A and B reduces (series-parallel) to $\frac{R}{3}$ → II → P.

(III) Circular network: by symmetry X, Y, Z and B are equipotential; the equivalent resistance between A and B is $\frac{4 R}{3}$ → III → S.

(IV) Series chain with the linking wire shorting part of it gives $\frac{2 R}{5}$ → IV → R.

Hence I → Q; II → P; III → S; IV → R, option (D).

Physics - Current Electricity Question with Solution | TestHub

Options:

Doubts & Discussion

List-I	List-II
(I)	(P) $\frac{R}{3}$
(II)	(Q) R
(III)	(R) $\frac{2 R}{5}$
(IV)	(S) $\frac{4 R}{3}$
	(T) $\frac{R}{2}$