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Reminder sheet

Real generators & loads

Bastaya

A real source has an internal resistance: its voltage drops as it delivers current. The generalised Ohm's law, U = E − r·I, tells that loss.

A real generator has an EMF E and an internal resistance r: when it delivers I, its terminal voltage drops to U = E − r·I. At no load U = E; in short circuit I_sc = E / r.

An active load (motor, charging battery) has a back-EMF E' and an internal resistance r': U = E' + r'·I. The power E'·I becomes mechanical or chemical, r'·I² is lost as heat. In a loop with generator and load: I = (E − E') / (r + r' + R).

Formulas

Real generatorU = E − r · I
QuantitySymbolUnit
EMFEV
Internal resistancerΩ
Terminal voltageUV
Active loadU = E' + r' · I
QuantitySymbolUnit
Back-EMFE'V
Internal resistancer'Ω
Generalised Ohm's lawI = ΣE − ΣE'ΣR
QuantitySymbolUnit
CurrentIA
Sum of loop resistancesΣRΩ
CharacteristicU = f(I) : droite de pente −r, ordonnée à l'origine E

Worked example

A cell of EMF E = 9 V and internal resistance r = 1.5 Ω supplies a resistor R = 28.5 Ω. What current does it deliver, what is its terminal voltage? What would the short-circuit current be?

Generalised Ohm's law: I = E / (r + R) = 9 / (1.5 + 28.5) = 0.3 A.

U = E − r · I = 9 − 1.5 × 0.3 = 8.55 V: the internal resistance "eats" 0.45 V.

In short circuit (R = 0): I_sc = E / r = 9 / 1.5 = 6 A, and all the power E·I heats the cell.

Common mistakes

  • Confusing E and U: the terminal voltage equals the EMF only at no load (I = 0).
  • Forgetting r in the loop: the current is E / (r + R), not E / R.
  • Getting the sign wrong for a load: it receives, so U = E' + r'·I (its voltage is larger than its back-EMF).

IEC symbols

+Cell / battery
GVoltage source
MMotor

Mini circuit

Open in the sandbox

Frequently asked questions

Why does the voltage of a cell drop when an appliance is connected?
Because a current flows through its internal resistance r and causes a drop r·I. The larger the current (or the older the cell, with a larger r), the more the voltage collapses.
How do I measure the internal resistance of a generator?
Take two points of the U = f(I) characteristic (for instance at no load and under load): r is the slope −ΔU/ΔI. Never with an ohmmeter, which must not be connected to a source.

36 exercises in this topic

This chapter is covered by the paths: General electricity, Measurement prep, ISL-oriented exercises

All sheets · All formulas · Glossary of electrical quantities · Standard electrical symbols (IEC 60617)

Practise this topic
Simulated time00:00:00
Q = I·t-
W = P·t-

Workbench

Circuit diagram CEI 60617

How does it work?

The perfboard: each big hole is a circuit node. You push a single leg of a component (resistor, lamp...) into it. The 4 small holes around it are connected to it: that is where chips and leads plug in.

  1. Drag a component onto the board: it snaps onto the grid. R rotates it.
  2. To join neighbouring big holes, click Jumper chip in the palette (or C) then drag on the board: a line of chips is laid at once. Bridged holes become a single node.
  3. For long links and for the power supply (placed next to the board), drag a lead from one big hole to another (or to a terminal).
  4. As soon as a loop is closed, the circuit is solved in real time (Ohm + Kirchhoff) and the diagram follows.
  5. Zoom with the wheel (or + / −, two-finger pinch); drag the background to pan, 0 fits the board. The + buttons around the board add a row or a column.

Del delete · R rotate · C chip brush · Esc cancel · wheel zoom · drag the background to pan

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