The essential answer
Load matching chooses an operating condition that extracts a particular response from a source. In the simple Thevenin model, an ideal fixed voltage source sits behind a fixed series resistance. A resistive load receives maximum power when its resistance equals that source resistance. This result is conditional: it does not automatically describe nonlinear, time-dependent, or actively regulated devices. It also does not maximize efficiency. The experiment should state whether the goal is peak power, useful voltage, long operation, or low internal dissipation.
How to reason about it
For the simple model, current is Vs/(Rs + RL), so load power is Vs squared times RL divided by (Rs + RL) squared. At very small load resistance the terminal voltage is small; at very large resistance the current is small. The intermediate optimum balances those effects. At equality, the load and internal resistance dissipate equal power, giving only half of the ideal source power to the load. Increasing load resistance improves that fraction while reducing delivered power. Real sources can shift during a sweep because of heating, polarization, illumination changes, or depletion. A single fitted resistance may then be an inadequate description. Test several loads in repeated or randomized order, allow a documented settling interval, and plot the complete voltage-current relation before interpreting an apparent optimum.
ILLUSTRATIVE · NOT A REPORTED RESULT
An example to work through
Assume an ideal 1.0 V source with a constant 100 ohm internal resistance. A 100 ohm load draws 5 mA and receives 2.5 mW. A 900 ohm load draws 1 mA and receives 0.9 mW, while internal dissipation is 0.1 mW. The second case delivers a smaller power but a larger share of the ideal-source output to the load: 90% rather than 50%. This comparison neglects converter overhead, temperature dependence, and changes in the source. It illustrates two different optimization goals rather than a universal recommendation.
Where interpretation fails
A fitted internal resistance is not always a fixed physical resistor. Treating a nonlinear biological or electrochemical source as a stationary battery can turn sweep history into an apparent matching law. Maximum-power operation can also accelerate depletion or alter the state being investigated.
The next decision
Choose the objective first. For characterization, report the power curve and settling protocol. For an application, include required terminal voltage, allowable duty cycle, and conversion overhead. Use the equality rule only when the fixed-source, fixed-series-resistance model adequately predicts the relevant range of loaded behavior.
Sources & context
These sources support the concepts noted below. Our synthetic examples and research framing are educational interpretation; they are not findings from these organizations or validation of our ventures.
- Maximum Power Transfer in a Circuit — MIT ↗
Fixed ideal voltage source plus series resistance maximum-power condition.
Source check: Official PDF search excerpt reviewed.
Educational research context, not a validated device specification or clinical protocol. Read our editorial and correction policy.