Workshop Calculation and Science: Units, Number Systems and Energy Costing
Scope of the paper
Workshop Calculation and Science tests the arithmetic and science a COPA technician applies at the bench and at the desk: fractions, percentage, ratio, mensuration, unit conversion, number-system arithmetic, basic electricity and energy costing.
Rules to keep
- Units: 1 inch = 25.4 mm; 1 litre = 1000 cm3; 1 kWh = 1 commercial unit = 3.6 MJ; 1 W = 1 J/s.
- Geometry: circle area = pi x r squared; cylinder volume = pi x r squared x h; rectangle area = length x breadth.
- Electricity: V = IR; P = VI = I squared x R = V squared / R; energy = power x time.
- Binary: 1's complement flips every bit; 2's complement adds 1 to the 1's complement and is how subtraction is performed.
Worked example
A desktop and monitor together draw 200 W and run 8 hours a day for 30 days. Energy = 200 x 8 x 30 = 48,000 Wh. Divide by 1000 to get 48 kWh, that is 48 units. At Rs 7 per unit the bill is 48 x 7 = Rs 336. The reasoning: watt-hours must become kilowatt-hours before the tariff is applied.
Quick check: the 2's complement of 5 in 4 bits. 5 = 0101; 1's complement = 1010; add 1 gives 1011, which represents -5.
Marks lost here
Stopping at watt-hours and quoting that figure as units; multiplying by 1000 instead of dividing; treating VA and W as equal (VA x power factor = W); mixing 1024 and 1000 prefixes; shifting the decimal point wrongly when turning a percentage into a multiplier, since 12% is 0.12.