Show how you would connect three resistors each of resistance 6 Ω, so that the combination has a resistance of 9 Ω. Also justify your answer.
Generated by claude-sonnet-4-6 · 2026-06-15 06:45 · grounding rag
Model Answer
Connect two resistors in parallel, then connect the third resistor in series with this parallel combination.
Justification:
Parallel combination of two 6 Ω resistors:
$$\frac{1}{R_p} = \frac{1}{6} + \frac{1}{6} = \frac{2}{6} \Rightarrow R_p = 3 \text{ Ω}$$
Total resistance (series with third resistor):
$$R = R_p + 6 = 3 + 6 = 9 \text{ Ω}$$
Source: Chapter 11, Section 11.6 (Resistors in Series and Parallel)
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Explanation
- The key idea: two 6 Ω in parallel give 3 Ω, and adding the third 6 Ω in series gives 3 + 6 = 9 Ω.
- Draw a small diagram if possible — examiners award marks for the circuit diagram + calculation together.
- Show both steps of calculation clearly; each step carries partial marks.