A resistor–inductor circuit (RL circuit), is an electric circuit consisting of resistors and inductors driven by a voltage or current source. A first order RL circuit is composed of one resistor and one inductor and is the simplest type of RL circuit.

Transients

In RL circuits , we have transients charging and discharging . For transients charging and discharging we need to have one resistor and one inductor in series. If we have more than one resistor in circuit , we may solve the circuit first by thevinin method, to find circuit equivalent resistance with respect to load (inductor in our case) .

For transients we can divide our discussion to different categories. We have two categories, in which we are interested to find the repose. Current and Voltage . The below table shows the different formula , for charging and discharge transients .

Charging Current Transient and Voltages

The value of current in I a inductor increases exponentially in a circuit. When it becomes fully charged, it starts behaving like a short circuit element . When an inductor is fully charged m the current voltage across it two terminal becomes zero, hence, as the inductor charges the voltage across the inductor drops. This behavior of current and voltage can be easily observed using an oscilloscope.

Example 1 :

For the following circuit sketch the current transient and Voltage Transient (charging) , for the given time

Solution

Discharging Current Transient and Voltages

The formula for the discharge transients for current and voltages are given below. These formulas can be used to find the behavior of a RL circuit. These formulas can be used to determine the voltage or current values at a particular time instant

v(L)=-E

it=

Example 2 

Sketch the transient behavior of current and voltage when , the switch is on position two for the following time instants . The time is in seconds