Series Circuits

Series Power Budget

resistor powers add

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

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=VIP = 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.

VIP2 V2 A4 W4 V2 A8 W8 V2 A16 W\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}
Series resistors split the battery budgetA single loop with a battery, an ammeter, and two resistors in the only path; voltage markers show the energy drops across the resistors.12 VA2 A2 ohm4 ohm2 A2 A2 A+-4 V+-8 Vheatheat

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.

VIP4 V1 A4 W4 V2 A8 W4 V3 A12 W\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}
Series resistors split the battery budgetA single loop with a battery, an ammeter, and two resistors in the only path; voltage markers show the energy drops across the resistors.12 VA2 A2 ohm4 ohm2 A2 A2 A+-4 V+-8 Vheatheat

Compute each resistor power

Ra uses 8 watts and Rb uses 16 watts.

partVIPRa4 V2 A8 WRb8 V2 A16 W\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}
Series resistors split the battery budgetA single loop with a battery, an ammeter, and two resistors in the only path; voltage markers show the energy drops across the resistors.12 VA2 A2 ohm4 ohm2 A2 A2 A+-4 V+-8 Vheatheat

The resistor powers add to the battery output

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

PRa+PRb=8 W+16 W=24 WP_{\text{Ra}} + P_{\text{Rb}} = 8\ \text{W} + 16\ \text{W} = \hl{24}\ \text{W}
Series resistors split the battery budgetA single loop with a battery, an ammeter, and two resistors in the only path; voltage markers show the energy drops across the resistors.12 VA2 A2 ohm4 ohm2 A2 A2 A+-4 V+-8 Vheatheat
electricity Each resistor spends part of the battery's power output, and the resistor powers add to the source power.