Chapter 38
LR Circuits
By connecting an inductor and a resistor together in series, we create anLR circuit. In an LR circuit, energy
is stored in the magnetic field of the inductor, and the resistor controls the rate at which current reaches the
inductor. The characteristic time scale required to create a full-strength magnetic field in the inductor is called
thetime constant , and is given by
D
L
R
: (38.1)
If the inductanceLis in henries and the resistanceRis in ohms, then the time constant will have units of
seconds.
Figure 38.1 shows an LR circuit. The circuit includes a battery, so that when the switchSis closed,
current flows through the resistor and inductor, and begins building up a magnetic field inside the coils of the
inductor. The resulting magnetic field will be in a direction that, by Lenz’s law, will tend to oppose changes
in the direction of the current, so that it becomes harder to increase the current. Once an amount of time has
gone by that is large compared to the time constant DL=R, the magnetic field in the inductor will have
essentially reached its maximum value, and the current will be constant.
Figure 38.2 shows the resistor voltage, inductor voltage, circuit current, and inductor magnetic flux in the
LR circuit as a function of time. The switchSis closed at timetD 0. Shortly afterwards, a small current
flows through the circuit, the voltage across the resistorRis equal zero, and the voltage across the inductor
is equal to the battery voltageV. At time DL=Rafter the switch is closed, the voltage across the resistor
RLSVFigure 38.1: An LR circuit.