In the circuit, the equivalent resistance between A and B is (Each resistance given in the diagram is R) :

CONCEPT:

• Equivalent resistance: It shows where the aggregate resistance connected either in parallel or series is calculated.
  • Essentially, the circuit is designed either in Series or Parallel.
  • Electrical resistance shows how much energy one needs when you move the charges/current through your devices.

Formula for resistors connected in series / parallel:

1. R = R1 + R2 + R3........(Series)
2. 1/R = 1/R1 + 1/R2 + 1/R3 ......(Parallel)

EXPLANATION:

Given that,

Value of all resistance is R and hence R1 = R2 = R3 = R4 = R5 = R

Identify the Junction points Between A and B and redraw the circuit.

Clearly, we can see R₂ is forming a Wheatstone bridge.

R₁ / R₃ = R / R = 1

R₅ / R₄ = R /R = 1

So, R₁ /R₃ = R₅ / R₄ So, it is a balanced Wheatstone bridge and hence no current will be in the PS branch.

R₁ and R₅ are in series equivalent = R + R = 2R

and R₃ and R₄ are in series, equivalent = R + R = 2R

Both are in parallel

So,

Req =(2R)² / 2R +2R = R

So, the equivalent resistance is R