PhysicsLAB Resource Lesson
RL Circuits

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RL Circuit
Let's begin by looking at an example of an inductor-resistance circuit, often referred to as an RL circuit.
When the switch is initially closed, I represents the current in the circuit and the inductor acts as a seat of "back emf."
We can write the following equation
where is the back emf induced by the coil to oppose the flux being created by the currents flowing through the solenoid.
Time Constant
As we did previously with RC circuits, we will now derive the time constant for this circuit. Since the inductor is intially opposing any changes in current, it will initially act to thwart the current flowing through the circuit, letting I = 0 when t = 0. In our derivaton, a lower case i represents transient current.  
The expression L/R is called the LR time constant.
Once a maximum current is reached, the inductor can no longer resist change and it effectively disappears - having no further impact on the circuit. Notice that if the battery were to be removed from the circuit, the current should ordinarily immediately fall to zero. However, when the switch is closed the inductor would once again want to resist the change in current. Consequently the current would fall off in agreement with an exponential decay as dictated by the time constant, L/R.

 How many many seconds will it take for the current in an RL circuit composed of a 36-volt battery, a 120-ohm resistor, and a 0.001-henry inductor to reach 90% of its final value?

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