31.7:
RL Circuits
An RL circuit essentially includes a resistor and an inductor either in series or parallel.
Consider a series RL circuit connected with a constant source of emf and a switch; here, the source is assumed to have zero internal resistance.
When the switch is closed, the current increases in the circuit, which leads to a potential difference across the resistor and inductor.
By applying Kirchhoff's loop rule, the rate of increase of current in the circuit can be determined.
Since the current was initially zero, the initial rate of change of current equals emf over inductance. Hence, the greater the inductance, the slower the current increases.
Over time, as the current increases in the circuit, the rate of current change approaches zero, finally leading to a steady state.
In this state, the final current in the circuit equals emf over resistance and does not depend on inductance. The same current is obtained even if the inductor is removed from the circuit.
31.7:
RL Circuits
An RL circuit consists of a resistor and an inductor and may have a source of emf connected to it. The inductor in the circuit helps to prevent rapid changes in current, which can be helpful if a steady current is required but the external source has a fluctuating emf. Consider an open RL circuit connected to a source of constant emf. As soon as the circuit is closed, the current begins to increase at a rate that depends only on the value of the inductance in the circuit. The greater the inductance, the more slowly the current increases. As the current increases in the circuit, the rate of increase of the current becomes smaller and smaller. This means that the current approaches a final, steady-state value. When the current reaches this value, its rate of increase is zero. The final current does not depend on the inductance; it is the same as it would be if the resistance alone were connected to the source with emf. After attaining the steady state, if the circuit is modified to bypass the battery, the current decays slowly and smoothly across the resistor and inductor. The time constant of an RL circuit is inductance over resistance. This measures how quickly the current builds toward its final value. For a given value of R, the time constant is greater for greater values of L. When L is small, the current rises rapidly to its final value; when L is large, it rises more slowly.
Suggested Reading
- Young, H.D. and Freedman, R.A. (2012). University Physics with Modern Physics. San Francisco, CA: Pearson. Pp. 1001.
- OpenStax. (2019). University Physics Vol. 2. [Web version]. Retrieved from 14.4 RL Circuits – University Physics Volume 2 | OpenStax