Series Power Budget - Electricity and Electronic Circuits Step by Step

The power spent in the series resistors adds to the power delivered by the battery.

electricity Each resistor spends part of the battery's power output, and the resistor powers add to the source power.

Example

The power spent in the series resistors adds to the power delivered by the battery. 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 voltage drop times current

Each resistor turns electrical energy into heat. Its power is the voltage drop across it times the current through it.

P = V I

At the same current, bigger drops make more power

Hold current at 2 amperes. More voltage drop means each coulomb spends more energy, so the resistor heats at a larger power.

\begin{array}{c|c|c}V & I & P \\2\ \text{V} & 2\ \text{A} & 4\ \text{W} \\4\ \text{V} & 2\ \text{A} & 8\ \text{W} \\8\ \text{V} & 2\ \text{A} & 16\ \text{W}\end{array}

At the same drop, bigger current makes more power

Now hold one resistor's drop at 4 volts and scan the current. More coulombs per second means more energy spent each second.

\begin{array}{c|c|c}V & I & P \\4\ \text{V} & 1\ \text{A} & 4\ \text{W} \\4\ \text{V} & 2\ \text{A} & 8\ \text{W} \\4\ \text{V} & 3\ \text{A} & 12\ \text{W}\end{array}

Compute each resistor power

Ra uses 8 watts and Rb uses 16 watts.

\begin{array}{c|c|c|c}\text{part} & V & I & P \\\text{Ra} & 4\ \text{V} & 2\ \text{A} & 8\ \text{W} \\\text{Rb} & 8\ \text{V} & 2\ \text{A} & 16\ \text{W}\end{array}

The resistor powers add to the battery output

The two resistor powers add to 24 watts, the same power delivered by the battery.

P_{\text{Ra}} + P_{\text{Rb}} = 8\ \text{W} + 16\ \text{W} = \hl{24}\ \text{W}