Add Energy across Power Intervals

Supplied materials

• Use the supplied fictional observations or model. Paper and pencil are optional; spoken answers are welcome. No equipment or real experiment is needed.

Learn the idea

A single power rating need not describe an entire day. When power is constant within each supplied interval, calculate each interval’s energy as power × time, then add the energies. Add watt-hours, not watt readings. This is a piecewise-constant model; an actual device could change power within an interval unless measurements support the assumption.

A fictional display uses 40 W for 3 h, 10 W for 2 h, and 0 W for the remaining 19 h. The intervals cover one 24-hour day and do not overlap. Energies are 120 Wh, 20 Wh, and 0 Wh, totaling 140 Wh = 0.14 kWh. The daily average power is 140 Wh / 24 h, about 5.83 W, which is different from its 40 W active-mode power.

1. Check that 3 + 2 + 19 = 24 hours.
2. Multiply power by duration separately for each mode.
3. Add the Wh values and divide by 1,000 for kWh.
4. Explain why adding 40 + 10 + 0 W would not give daily energy.

Check your reasoning

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Take it further

Change the 5 W mode to 2 W for the same 20 h. Daily energy becomes 120 + 40 = 160 Wh = 0.16 kWh, 0.06 kWh below the prior case.

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