32
Problem solving
Textbook: pp. 94–95
GoalSolve problems on the work and power of current: choose a formula, match units and calculate energy use.
New words
choosing a formula · formulani tanlashenergy consumption · energiya sarfipower rating · quvvat jadvalimatching units · birliklarni moslash
Explanation
Choose the formula by what is given: P = IU if I and U are given; P = I²R if I and R; P = U²/R if U and R. For work use A = Pt or A = IUt. Convert time to seconds (for joules) or hours (for kW·h), and power to watts or kilowatts: 1 kW = 1000 W, 1 h = 3600 s. The power marking on devices such as heaters and lamps refers to their normal working mode. After getting an answer check that its size makes sense. The devices in the problems are for calculation only: do not work with the mains without adults.
Worked examples
A lamp on a 220 V supply draws 0.25 A: P = 0.25 · 220 = 55 W. In 4 hours A = 55 W · 4 h = 220 W·h = 0.22 kW·h.
A heating coil has R = 44 Ω at U = 220 V: P = U²/R = 220² : 44 = 48400 : 44 = 1100 W. In 2 hours 1.1 kW · 2 h = 2.2 kW·h.
Class activity
With an adult copy the power markings of 3 household devices into your notebook and calculate each one’s 2-hour consumption in kW·h. Do not touch the devices, only read the label.
Practice
1
When is the formula P = I²R convenient?
When the current and the resistance are known.
2
An iron has R = 55 Ω at U = 220 V. Its power in W?
880
3
A 1.2 kW device ran for 5 hours. How many kW·h were used?
6
4
Why does a device with smaller R have a larger power at the same voltage?
P = U²/R: with smaller R the current and the power are larger.