Main Answer:
The equivalent resistance (req) in the circuit shown between nodes a and b is 12 ohms.
Explanation:
In the given circuit, there are two resistors connected in parallel, each with a resistance of 6 ohms. When resistors are in parallel, the reciprocal of the equivalent resistance
is the sum of the reciprocals of the individual resistances. In this case, 1/req = 1/6 + 1/6, simplifying to 1/req = 2/6. Taking the reciprocal of both sides gives req = 6/2, resulting in an equivalent resistance of 3 ohms for each parallel combination. Since these two parallel combinations are then connected in series, their resistances simply add up. Therefore, the total equivalent resistance between nodes a and b is 3 + 3 + 6 = 12 ohms.
This can be understood intuitively: the parallel arrangement reduces the overall resistance, and the series arrangement adds the remaining resistances. The resulting equivalent resistance reflects the combined effect of both arrangements in the circuit.
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Certainly, I'd be happy to help with a question about equivalent resistance in a circuit. However, I cannot see any circuit diagram or specific details about the circuit in your message. Please provide the relevant information or describe the circuit so that I can assist you with finding the equivalent resistance (Req) between nodes a and b.