Tricky Circuit

Internal resistance and useful power

Why a battery sags

Internal resistance is the opposition to current inside a source: it makes terminal voltage fall under load. A load is the circuit using the energy; a milliampere (mA) is one thousandth of an ampere, and a watt (W) measures power.

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EXPERIMENT BENCH

Change the circuit settings, predict the readings, then check a challenge. These are learning models, with the assumptions explained in each lesson.

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Why it works

One ideal voltage source plus a fixed internal resistor. Battery chemistry, state of charge, heating and runtime are not simulated.

Vs is source voltage, Ri internal resistance, RL load resistance and I current. I = Vs/(Ri + RL); load voltage = I × RL. Load power = I² × RL; internal loss = I² × Ri.

Difficulty

  1. Build · Build it

    Power on at 9 V, internal resistance 2 Ω and load 100 Ω. Read about 8.824 V.

    Need a hint?

    Vs = 9 V; Ri = 2 Ω; RL = 100 Ω → 8.824 V

  2. Explore · Change one thing

    At 9 V and internal resistance 5 Ω, keep load voltage at least 8.5 V and current at least 50 mA.

    Need a hint?

    Vs = 9 V; Ri = 5 Ω; RL = 100 Ω → 8.571 V; 85.714 mA

  3. Solve it · Solve the challenge

    At 9 V and internal resistance 10 Ω, deliver 1.2–1.4 W to the load with internal loss at most 0.35 W.

    Need a hint?

    Vs = 9 V; Ri = 10 Ω; RL = 40 Ω → 1.296 W; 0.324 W

Extra reading and circuit recipes

Why a battery sags

A useful pattern

A source can look healthy with no load yet sag when current flows: a voltage reading alone does not reveal its internal resistance.

Beyond the model

With positive Ri and unconstrained load values, maximum load power in this model occurs when RL = Ri. Half the supplied power is then lost internally, so maximum power is not maximum efficiency; the slider may not reach this condition.

A useful trap to avoid

A smaller load resistance asks for more current; it does not mean a smaller electrical burden.

Internal resistance increases while source voltage and load stay fixed. Load voltage…

  1. rises
  2. falls
  3. stays unchanged
Read more

More resistance in the series path reduces current, so I × RL falls.

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