A wire of resistance R is cut into three equal parts. If these three parts are then joined in parallel, calculate the total resistance of the combination so formed.
Generated by claude-sonnet-4-6 · 2026-06-15 06:42 · grounding rag
Model Answer
When wire of resistance R is cut into three equal parts, each part has resistance = R/3.
When these three parts are connected in parallel:
$$\frac{1}{R_p} = \frac{1}{R/3} + \frac{1}{R/3} + \frac{1}{R/3} = \frac{3}{R} + \frac{3}{R} + \frac{3}{R} = \frac{9}{R}$$
$$\therefore R_p = \frac{R}{9}$$
The total resistance of the combination is R/9.
Source: Chapter 11, Section 11.6.2 – Resistors in Parallel
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Explanation
- Step 1 (1 mark): Each part has resistance R/3 (resistance is proportional to length, so cutting into 3 equal parts gives R/3 each).
- Step 2 (1 mark): Apply the parallel formula $\frac{1}{R_p} = \frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}$ to get R/9.
- Examiners want both steps shown clearly. Simply writing R/9 without working will lose the method mark.