Power and Energy

Electric Power

voltage times current

Electric power is the rate of energy transfer. In a circuit, voltage times current gives power.

Example

Electric power is the rate of energy transfer. In a circuit, voltage times current gives power. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Power is energy each second

Electric power tells how fast electrical energy is being delivered or spent. A watt is a joule each second.

P=EtP = \frac{E}{t}

For a circuit, power is voltage times current

Voltage is energy per charge, and current is charge per second. Multiplying them gives energy per second, which is power.

P=VIP = V I

Fixed current makes power track voltage

Hold the current at 3 amperes. Higher voltage gives each coulomb more energy, so the same charge flow delivers more watts.

VIP4 V3 A12 W8 V3 A24 W12 V3 A36 W\begin{array}{c|c|c}V & I & P \\4\ \text{V} & 3\ \text{A} & 12\ \text{W} \\8\ \text{V} & 3\ \text{A} & 24\ \text{W} \\12\ \text{V} & 3\ \text{A} & 36\ \text{W}\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 A

Fixed voltage makes power track current

Now hold the voltage at 12 volts. More coulombs per second means more energy delivered each second, so power rises with current.

VIP12 V1 A12 W12 V2 A24 W12 V3 A36 W\begin{array}{c|c|c}V & I & P \\12\ \text{V} & 1\ \text{A} & 12\ \text{W} \\12\ \text{V} & 2\ \text{A} & 24\ \text{W} \\12\ \text{V} & 3\ \text{A} & 36\ \text{W}\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 A

Compute the power

The battery supplies voltage and current together, so multiplying gives 36 watts.

P=12 V⋅3 A=36 WP = 12\ \text{V} \cdot 3\ \text{A} = \hl{36}\ \text{W}
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 A
electricity A 12 V source delivering 3 A supplies 36 W of electrical power.