Power and Energy

Energy Over Time

power accumulates

Power is energy per second, so power multiplied by time gives total energy transferred.

Example

Power is energy per second, so power multiplied by time gives total energy transferred. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Energy is power times time

Power is a rate. If a circuit spends power for a time, the total energy transferred is power times time.

E=PtE = P t

Fixed power accumulates energy over time

Hold the power at 36 watts. Longer run time stacks up more joules at the same steady rate.

PtE36 W5 s180 J36 W10 s360 J36 W15 s540 J\begin{array}{c|c|c}P & t & E \\36\ \text{W} & 5\ \text{s} & 180\ \text{J} \\36\ \text{W} & 10\ \text{s} & 360\ \text{J} \\36\ \text{W} & 15\ \text{s} & 540\ \text{J}\end{array}
A resistor turns electrical power into heatA single loop with a battery, an ammeter, and a resistor carrying current; the resistor is the load where energy is spent.12 VA3 A4 ohm3 Aheat

Fixed time turns more power into more energy

Now hold the run time at 10 seconds. More watts means more joules per second, so the energy total rises with power.

PtE12 W10 s120 J24 W10 s240 J36 W10 s360 J\begin{array}{c|c|c}P & t & E \\12\ \text{W} & 10\ \text{s} & 120\ \text{J} \\24\ \text{W} & 10\ \text{s} & 240\ \text{J} \\36\ \text{W} & 10\ \text{s} & 360\ \text{J}\end{array}
A resistor turns electrical power into heatA single loop with a battery, an ammeter, and a resistor carrying current; the resistor is the load where energy is spent.12 VA3 A4 ohm3 Aheat

Substitute the power and time

Use the 36 watt power for 10 seconds.

E=36 W⋅10 sE = 36\ \text{W} \cdot 10\ \text{s}
A resistor turns electrical power into heatA single loop with a battery, an ammeter, and a resistor carrying current; the resistor is the load where energy is spent.12 VA3 A4 ohm3 Aheat

Compute the energy

The resistor transfers 360 joules of energy over that time.

E=360 JE = \hl{360}\ \text{J}
A resistor turns electrical power into heatA single loop with a battery, an ammeter, and a resistor carrying current; the resistor is the load where energy is spent.12 VA3 A4 ohm3 Aheat
electricity A 36 W resistor running for 10 s transfers 360 J of energy.