Question

The equivalent resistance between A and B is _________.

• A. $\frac{2}{3} \Omega$
• B. $\frac{3}{2} \Omega$
• C. $\frac{1}{3} \Omega$
• D. $\frac{1}{2} \Omega$

Answer 1

The Correct Option is A

The problem requires calculating the equivalent resistance between points A and B in a complex circuit involving combinations of resistors. To find the equivalent resistance, we identify series and parallel connections of resistors and simplify step by step.

The circuit can be simplified as follows: 

1. The resistors between A and B include combinations that can be reduced using the series and parallel formulas:
   • Parallel Resistance Formula: \(R_{p} = \frac{R_{1} \cdot R_{2}}{R_{1} + R_{2}}\)
   • Series Resistance Formula: \(R_{s} = R_{1} + R_{2}\)
2. First, notice the symmetry in the circuit: each side can be reduced independently.
3. The resistors in parallel pairs, for instance, \(1.5 \, \Omega\) and \(0.5 \, \Omega\), should be calculated first using the parallel resistance formula:
4. Similarly, perform the parallel calculation for the \(8 \, \Omega\) and \(2 \, \Omega\), as well as other pairs.
5. After finding parallel resistances, calculate the series resistance of these reduced groups.
6. Once all combinations are reduced, calculate the total equivalent resistance as:
   • \(R_{eq} = R_{th\_path1} + R_{th\_path2} + ...\text{(combining results)}...\)

Using these calculations, the equivalent resistance between A and B is found to be \(\frac{2}{3} \, \Omega\), which corresponds to the correct option.