Question

Find equivalent resistance
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Answer 1

Given :

Five equal resistances of R are connected as shown in the figure.

To Find :

We are asked to find equivalent resistance between A and B.

Solution :

In these kind of questions, first step which is to be done is to simplify the circuit.

See the attachment for better understanding.

» In the upper branch, two resistors are connected in series$.$

Hence their equivalent resistance will be 2R.

Similarly resistance of lower branch will also be 2R.

Finally three resistances of 2R, R and R come in parallel.

Hence net equivalent resistance of the circuit will be

➙ 1/Req = 1/R₁ + 1/R₂ + 1/R₃

➙ 1/Req = 1/2R + 1/R + 1/2R

➙ 1/Req = 2/2R + 1/R

➙ 1/Req = 1/R + 1/R

➙ 1/Req = 2/R

➙ Req = R/2

Answer 2

Given :

Five equal resistances of R are connected as shown in the figure.

To Find :

We are asked to find equivalent resistance between A and B.

Solution :

In these kind of questions, first step which is to be done is to simplify the circuit.

See the attachment for better understanding.

» In the upper branch, two resistors are connected in series$.$

Hence their equivalent resistance will be 2R.

Similarly resistance of lower branch will also be 2R.

Finally three resistances of 2R, R and R come in parallel.

Hence net equivalent resistance of the circuit will be

➙ 1/Req = 1/R₁ + 1/R₂ + 1/R₃

➙ 1/Req = 1/2R + 1/R + 1/2R

➙ 1/Req = 2/2R + 1/R

➙ 1/Req = 1/R + 1/R

➙ 1/Req = 2/R

➙ Req = R/2