To calculate the equivalent resistance across the two ends A and B of the circuit, we need to follow the below steps:



Firstly, we need to simplify the circuit by combining the resistors that are in series and in parallel. We can simplify the circuit as follows:

- The two resistors (6Ω and 12Ω) in parallel can be combined using the formula for the equivalent resistance of resistors in parallel:

1/R = 1/6 + 1/12 = 1/4

R = 4Ω

- The resistor (2Ω) and the equivalent resistance (4Ω) in series can be combined using the formula for the equivalent resistance of resistors in series:

R = 2 + 4 = 6Ω

- The two resistors (3Ω and 6Ω) in parallel can be combined using the formula for the equivalent resistance of resistors in parallel:

1/R = 1/3 + 1/6 = 1/2

R = 2Ω



Now, we have only two resistors (6Ω and 2Ω) left in the circuit. These two resistors are in series, so we can combine them using the formula for the equivalent resistance of resistors in series:

R = 6 + 2 = 8Ω

Therefore, the equivalent resistance across the two ends A and B of the circuit is 8Ω.



- In the first step, we simplified the circuit by combining the resistors that are in series and in parallel. This step reduces the complexity of the circuit and makes it easier to calculate the equivalent resistance.
- In the second step, we combined the remaining resistors in the circuit using the formula for the equivalent resistance of resistors in series. This step gives us the final equivalent resistance across the two ends A and B of the circuit.
- Overall, the key to calculating the equivalent resistance of a circuit is to simplify the circuit by combining the resistors that are in series and in parallel and then use the formula for the equivalent resistance of resistors in series or parallel to combine the remaining resistors.