Maths for electricians · Topic 6 of 6

Percentages, ratios and efficiency

About 3 minutes · Worked examples and a mini test

Percentages turn up in voltage drop limits, efficiency, test readings and pricing a job. Get comfortable with the three basic moves below.

• V – Voltage
• R – Resistance
• P – Power

The three moves

• A percentage of a number: multiply by the percentage and divide by 100. 5 % of 230 V = 230 × 5 ÷ 100 = 11.5 V.
• One number as a percentage of another: divide, then multiply by 100. A 9.2 V drop on 230 V is 9.2 ÷ 230 × 100 = 4 %.
• Increase by a percentage: multiply by (1 + the percentage as a decimal). £50 plus 20 % VAT = 50 × 1.2 = £60.

Efficiency

Efficiency = output ÷ input × 100 %

A motor taking 2,000 W and delivering 1,700 W of mechanical power is 1,700 ÷ 2,000 × 100 = 85 % efficient. The missing 15 % is lost as heat and noise.

Ratios

A ratio compares two quantities. A transformer with a turns ratio of 10:1 steps 230 V down to 230 ÷ 10 = 23 V.

Real uses

• Voltage drop: 3 % for lighting (6.9 V) and 5 % for other circuits (11.5 V) on 230 V.
• The 80 % rule for Zs: a B32's 1.37 Ω × 0.8 = 1.10 Ω for a test reading. See the Max Zs table.

Exam tip: to find 80 % of something, multiply by 0.8. To find what's left after 15 % is lost, multiply by 0.85.

Try it: Voltage drop calculator