# Inductors in DC Circuits

A resistor and inductor are used to create a basic DC circuit. We want to know how this inductor affects the circuit.

Constantly, an inductor’s effect in an electric circuit is to counteract the effect of a voltage or current source acting to alter the circuit current. When a switch is closed, the circuit’s voltage and resistance combine to determine how much current flows through the switch.

An inductor is one that resists change in current. The current in a DC circuit tends to stabilize after a brief period of variation, at which point it remains constant.

• Similar to how adding a flexible tank (reservoir) to a hydraulic pipeline can increase its capacity, an inductor in an electric circuit can do the same for a current. The tank’s volume shifts as it expands.
• When the pipeline’s shutoff valve is turned to the “open” position, water flows into a flexible reservoir first, before continuing on its normal path. As a result, the reservoir is being filled in part by the flow.
• When the storage tank is full, the pipeline resumes its regular water delivery. That is to say, there is some initial resistance and limitation of the water flow, but the current is then stable and unchanging.
• An inductor’s function in an electric circuit is to act against a shift in the current through the circuit (keeping the current unchanged).
• Once again, knowing how long it takes for the electric current in Figure 1b to reach its constant value or the water in Figure 2b to return to its normal flow would be interesting.

We can define a time constant (much like the case for a capacitor) in terms of the resistance R and inductance L values in a circuit in the following way:

The time constant is expressed in seconds if L is in henries and R is in ohms. This equation suggests that the inductor’s effect will last longer for lower values of R. The current takes about 5 the time constant to stabilize at a fixed value.

## RL Circuit Time Constant Calculation Example

In a series circuit with a resistor and a coil, what is the time constant? With an inductance of 11 mH and a resistance of 4 Ω, the coil complements the resistor’s 51Ω  value nicely.

Solution

As a result of making the necessary changes to Equation 1, we have

After about 5 times the time constant, an inductor’s influence in a DC electric circuit disappears.

## RL Circuit Time Constant

An inductor’s inherent ability to store electrical energy has the same effect on a circuit as a capacitor’s, delaying the rate at which the voltage across the circuit changes. However, an inductor’s delay is caused by the component’s resistance to a change in the circuit’s current.

If you have an inductor and a resistor in a circuit, the time constant is

The time constant is expressed in seconds when L is in henries and R is in ohms.

What was said about the delay in the voltage-changing components of a circuit that also included capacitors and resistors, and the corresponding graphs, also applies to a circuit that includes an inductor. Current changes in a circuit rather than voltage changes are represented by the values and percentages shown at the end of periods T, 2T, 3T, etc.