Question

consider the following circuit diagram if R1 = R2=R3=R4=R5=3 ohm . find equivalent resistance of the circuit (Please give full solution)

Answer 1

R2 and R3 are in series so R23 = R2+R3 = 3+3 =6ohm

R23 is in parallel with R4 = 1/R234 = 1/6 + 1/3 = 1/2
R234 = 2 ohm

R1 , R5 and R234 is in series so R' = 3+3+2 = 8ohm



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Answer 2

Given:

An arrangement of 5 resistors with resistance 3Ω each

To Find:

The equivalent resistance of the circuit

Solution:

Two resistors are in series when they have one point in common. The equivalent resistance in series is the sum of the individual resistors.

Two resistors are in parallel when they have two points in common. The reciprocal of the equivalent resistance in parallel is equal to the sum of the reciprocal of the individual resistors.

In the given circuit, R₂ and R₃ are attached in series. So their net resistance R₂₃ = 3Ω + 3Ω = 6Ω.

Now, R₂₃ is in parallel with R₄. The equivalent resistance R₂₃₄ = $\frac{R_2_3R_4}{R_2_3+R_4}$

 = 6 X 3 / 6 + 3

= 2 Ω

R₂₃₄ is in series with R₁ and R₅

So the equivalent resistance of the circuit = R₂₃₄ + R₁ + R₅

= 2 + 3 + 3

= 8Ω

Hence, the equivalent resistance of the circuit is 8Ω.