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The CSA ratio: working out r2 before you measure itCan you know r2 before you measure it?

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The question at the end: Can you know r2 before you measure it? The answer is in the notes below.

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This is worth real time, because it is how you know whether your reading is right. If you know r1, you can work out what r2 should be from the ratio of the two conductor sizes.

r2 = r1 × (line csa ÷ cpc csa)

Twin and earth comes in fixed pairings, so the ratios are worth knowing:

CableLine ÷ cpcRatioTypical circuit
1.0 / 1.0 mm²1 ÷ 11Lighting
2.5 / 1.5 mm²2.5 ÷ 1.51.67Socket ring
4 / 1.5 mm²4 ÷ 1.52.67Socket radial
6 / 2.5 mm²6 ÷ 2.52.4Cooker
10 / 4 mm²10 ÷ 42.5Shower
16 / 6 mm²16 ÷ 62.67Larger loads

4 mm² line with a 1.5 mm² cpc, r1 measured at 0.3 Ω

Ratio = 4 ÷ 1.5 = 2.67

r2 = 0.3 × 2.67
   = 0.8 Ω expected

So before the meter goes anywhere near the cpc, you already know you are looking for about 0.8 Ω. If it comes back at 2 Ω, something is wrong — and you know it immediately rather than three circuits later.

Why the cpc is always the higher number. Hold a piece of twin and earth and look at it: the copper in the brown is visibly thicker than the bare earth. Less copper means more resistance, so a 1.5 mm² cpc beside a 4 mm² line has 2.67 times the resistance over the same length.
✋Inversely, not directly. Easy to get backwards. Resistance is inversely proportional to cross-sectional area — it falls as the conductor gets bigger and rises as it gets smaller.
r₂ = r₁ × (line csa ÷ cpc csa) A thinner cpc has more resistance — so r₂ is always the bigger number. 1.0 / 1.0 × 1 lighting 2.5 / 1.5 × 1.67 socket ring 4 / 1.5 × 2.67 socket radial 6 / 2.5 × 2.4 cooker Line in brown, cpc in green. Drawn to scale — the size difference is the whole point.
Know r₁ and you know what r₂ should be before the meter tells you. If the measured r₂ is a long way off the ratio, something is wrong.

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