RL and RC Time Constants.

Recall that in our lamp and cap circuit, the lamp lights up for a second, but then goes out. What determines how long the lamp stays lit? The lamp is not a perfect device which generates light from electricity. It has losses, and shows electrical friction (read: resistance). Any time that you have a resistor and a capacitor in a circuit, we call it an RC circuit. Likewise, if there is a resistor and a coil in a circuit, we call it an RL circuit.

In this circuit, the moment the battery is applied, current starts to flow through the resistor, and a voltage begins to build up across the plates of the capacitor. The amount of time that it takes for the voltage across the capacitor plates to reach the voltage of the battery, is a result of the values of the capacitor and the resistor. The larger these two values are, the longer it will take for the entire voltage to appear across the cap. This relationship is expressed by a formula, and is called "Time Constant". The formula is:


T = RC
where T= Time in seconds, R=resistance in ohms, and C=capacitance in farads.

A time constant also exists between coils and resistors, however, because of the nature of how a coil is made (it is essentially a piece of wire), time constants in RL circuits are much smaller. Recall that earlier in the course, we discussed that inductors and capacitors are almost exact opposites. Here is another formula which will seem re-hashed.

T = L / R
where T= Time in seconds, R=resistance in ohms, and L=inductance in henries.

Remember this formula?
X_L = 2pfL


Well, you are going to have to start using X_L and X_C again. Because we are going to begin using capacitors and coils in the same circuit. Now the real fun of electronics begins.