Physics · Circuits

Internal Resistance and Terminal Voltage

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Wrap-up

What you learned

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Read next: Power and Energy in CircuitsCompare steady load power

Key takeaway

Terminal voltage is the voltage that actually reaches the load, so under load it is V_terminal = E - I r.
A larger current means a larger internal voltage drop and more power wasted inside the source.

Common misconception

If a battery is labeled 12 V, the load must always receive 12 V no matter what is connected to it.

The 12 V label is the emf, not necessarily the terminal voltage under load.

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Reference and support

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Equation snapshotLoop current with internal resistance · Terminal voltageShow 2 equations

Loop current with internal resistance
$I = \frac{E}{R + r}$
The current is set by the emf and the total loop resistance from both the load and the source.
Terminal voltage
$V_{terminal} = E - I r = I R$
Terminal voltage is what remains for the load after the internal drop is taken from the emf.

Why it behaves this way

Explanation

A real source is not just an ideal emf. When current flows through its internal resistance, part of the source rise is spent inside the source, so the terminal voltage available to the load becomes smaller than the emf.

This bench stays intentionally bounded: one source with emf E and internal resistance r drives one load resistance R. That is enough to show why heavy loads pull the terminal voltage down, why the source wastes power internally, and why the ideal-source limit is still useful without pretending every battery is perfect.

Key ideas

01Current depends on the total loop resistance E / (R + r), not on the load resistance alone.

02Terminal voltage is the voltage that actually reaches the load, so under load it is V_terminal = E - I r.

03A larger current means a larger internal voltage drop and more power wasted inside the source.

Worked examples

Live source checks

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Frozen walkthrough

Step through the frozen example

Frozen walkthrough

Use the exact source and load on screen. The same emf, internal resistance, and load resistance drive the live loop, the readout card, and the response graphs below.

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Example 1 of 2

Frozen valuesUsing frozen parameters

For the current non-ideal source and load, what current flows and what terminal voltage does the load actually receive?

E

Source emf

12 V

r

Internal resistance

1 ohm

R

Load resistance

6 ohm

1. Build the full loop resistance

R_{total} = R + r = 6 + 1

2. Use the full loop current rule

I = \frac{E}{R + r} = \frac{1}{2} 6 + 1 = 1.71

3. Read the load voltage honestly

V_{terminal} = I R = 1.71 \times 6 = 10.29

4. Check the internal drop

The source loses

I r = 1.71 \times 1 = 1.71

inside itself, so

E - I r = 10.29

Current and terminal voltage

I = 1.71, V_{terminal} = 10.29

This setup still loses some voltage inside the source, but the terminal voltage remains easy to compare against the emf.

Quick test

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Accessibility

Open the text-first descriptions when you need the simulation and graph translated into words.

The simulation shows one battery with emf and one internal resistor on the same top wire, followed by one external load resistor and one return path. Sliders set emf, internal resistance, and load resistance.

Overlays can show current flow, voltage labels, the power split between the load and the source interior, and an ideal-source reference cue. The readout card and both graphs update from the same one-loop source-load model.

Graph summary

The terminal-response graph sweeps load resistance and shows terminal voltage together with the internal drop on one voltage scale. The power-split graph uses the same sweep to compare power delivered to the load with power lost inside the source.

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