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The equivalent resistance between points A and B shown in the figure below:
Question

The equivalent resistance between points A and B shown in the figure below:

A.

2 Ω

B.

6 Ω

C.

9 Ω

D.

4.5 Ω

Correct option is A

(a) The equivalent resistance between points A and B is 2 Ω.

To calculate the equivalent resistance between points A and B:

  1. The resistors form a combination of parallel and series connections.
  2. The 3 Ω and 3 Ω resistors at the top are in series Rseries=3+3=6Ω
  3. This combined resistance of 6Ω6 \, \Omega6Ω is in parallel with the other 6Ω6 \, \Omega resistor.

RTotal= (1/6)+(1/3)

                    RTotal = 2Ω 

  1. Series Combination: Total resistance increases (Rtotal=R1+R2R_{\text{total}} = R_1 + R_2Rtotal=R1+R2).
  2. Parallel Combination: Total resistance decreases (Rtotal = 1/R1+1/R2)
  3. Solving step-by-step is crucial for mixed combinations of resistors.
  4. Equivalent resistance reduces when combining in parallel.
  5. Simplify series and parallel resistances sequentially.

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