Question

hi, kindly find the answer.

Q3. Find the equivalent resistance between point-A and point-B for given circuit if all resistors are identical of r22 win www w WW WW WWW w -WW- w r r www (A) 5r 12 7r (B) 12 (C) 9r 11 5r (D) 11

Answer 1

We will solve this problem by finding the equipotential points.

Our terminals are A and B.

The remaining junctions are named as P, Q, R, S, and T for the sake of simplicity in the diagram below:

an ho S TO so Er te Er Y 7 no C A . B

We will find the equipotential points by preparing a chart and will compare which columns are the same.

The numbers used are nothing but the number of resistors coming in the path from terminal to respective junctions.

	P	Q	R	S	T	U
A	2	1	2	3	1	2
B	3	2	1	2	2	1

From the chart, we can see, the points Q and T are equipotential points and the points R and U are equipotential points.

After short-circuiting the equipotential points, the circuit would look like :

S M RU QT A B M

Now, our diagram looks much simpler consisting of series and parallel combinations.

The equivalent resistance between P and Q,T is r/2.

The equivalent resistance between S and R,U is r/2.

The equivalent resistance between A and Q,T is r/2.

The equivalent resistance between B and R,U is r/2.

The equivalent resistance between Q,T and R,U is r/2.

See the diagram below, after replacing the equivalent resistance:

S e 0 이고 국인 허 0,1 RO A5 이

Now, our diagram is further getting simpler.

The equivalent resistance between Q,T and R,U from the other side is r/2 + r + r/2 = 2r.

See the next diagram below:

8/2 8/2 7 8/2 SIT AS 13 RU

Now, we have two parallel resistors between Q,T and R,U. Their equivalent resistance is $(\frac{2}{r}+\frac{1}{2r})^{-1}=\frac{2r}{5}$ .

See the next diagram below:

2015 r ½ B) /

Now, we have three resistors in series between A and B along one path. their equivalent resistance is 2r/5 + r/2 + r/2 = 7r/5.

See the next diagram below:

SIE SA SB

Now we have only two resistors in parallel between A and B. Their equivalent resistance is $(\frac{1}{r}+\frac{5}{7r})^{-1}=\frac{7r}{12}$ .

Therefore, the equivalent resistance between A and B is 7r/12.[answer]

correct option is (B).