Electricity and magnetism

Ohm’s law for a complete circuit and EMF

In a closed circuit with internal resistance r, current is emf divided by total resistance: $I=\mathcal E/(R+r)$.

In a closed circuit with internal resistance r, current is emf divided by total resistance: $I=\mathcal E/(R+r)$.

A real source and terminal voltage

The emf $\mathcal E$ is energy supplied by the source per coulomb, measured in volts; it is not generally the terminal voltage while the source delivers current. For external resistance $R$ and internal resistance $r$, the complete-circuit law is $I=\mathcal E/(R+r)$. During discharge, terminal voltage is $U=IR=\mathcal E-Ir$. With an open circuit, $I=0$ and terminal voltage equals $\mathcal E$.

Current in a closed circuit is limited by both the external load and the source’s internal resistance. As $R$ increases, current falls and terminal voltage $U=\mathcal E-Ir$ approaches the emf. Under a short circuit, $R\to0$, but current is not infinite when $r>0$: $I_{sc}=\mathcal E/r$. A 12 V source with $r=1.0\,\Omega$, for example, has an ideal short-circuit current of 12 A—large enough to cause overheating.

Measure $U$ while the source is supplying a load to distinguish emf from the voltage actually available externally. If the load receives $P=UI$, the source internally dissipates $I^2r$.

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