RC Discharge Circuit

In this article of our series we will see the RC discharge circuit. In the previous RC charging circuit tutorial, we saw how a capacitor is charged from the resistance until it reaches a period equal to the 5 time constants of C, known as 5t, and then it continues to fully charge as long as a constant feed is applied.

If this fully charged capacitor is now separated from the DC battery supply voltage, the stored energy accumulated during the charging process will remain indefinitely on its plates (assuming an ideal capacitor and ignoring any internal loss). Keeps the voltage stored along the connection terminals at a constant value.

If the battery has been replaced by a short circuit, the capacitor will come back from resistance when the switch is switched off, since we now have an RC Discharge circuit. When the capacitor discharges the current from the serial resistance, the stored energy inside the capacitor is discharged with Vc voltage throughout the decaying capacitor up to zero, as shown below.

RC Discharge Circuit

RC Discharge Circuit

As we saw in the previous training, the time constant ( τ ) in an RC Discharge circuit is still equal to 63%. Then, after 1t, a time constant for an RC Discharge circuit that was initially fully charged, the voltage in the capacitor decreased by 63% of the initial value, which is 1 – 0.63 = 0.37 or 37% of its final value.

Therefore, the time constant of the circuit is given as the time it takes for the capacitor to discharge up to 63% of its fully charged value. Therefore, a time constant for an RC discharge circuit is given as voltage along the plates representing 37% of its final value. Its final value is zero volts (completely discharged) and in our curve this is given as 0.37 Vs.

As the capacitor discharges, it does not lose its charge at a constant rate. At the beginning of the discharge process, the initial conditions of the circuit are: t = 0, i = 0 and q = q. the voltage along the capacitor plates is equal to the supply voltage and VC = VS. Since the voltage at t = 0 is the highest value along the capacitor plates, the maximum discharge current therefore flows around the RC circuit.

RC Discharge Circuit Curves

RC Discharge Circuit

When the switch is first turned off, the capacitor begins to empty, as shown in the picture. The degradation rate of the RC Discharge curve is initially steeper. Because the discharge speed is the fastest at the beginning, but the capacitor shrinks exponentially because it loses the load at a slower rate. As the discharge continues, the VC decreases and results in less discharge current.

In the previous RC charging circuit, we found that the voltage on capacitor C was equal to 0.5Vc at 0.7T, and the stable state completely discharge value was finally achieved at 5T. For an RC discharge circuit, the voltage on the capacitor (VC) is defined as a function of time during the discharge period as follows:

RC Discharge Circuit

VC is the voltage along the capacitor.
VS supply is voltage.
t is the time since the removal of the supply voltage.
RC is the time constant of the RC Discharge circuit.
As with the previous RC charging circuit, we can say that in an RC discharge circuit, a capacitor itself is given to a time constant as follows:

RC Discharge Circuit

Here, R is Ω and farads are C.

Therefore, in the table below we can show the percentage voltage and current values for the capacitor in an RC Discharge circuit for a specific time constant.

RC Discharge Table

RC Discharge Circuit

Since the discharge curve for an RC discharge circuit is exponencial, for all practical purposes, it is considered that the capacitor is completely discharged after five time constants.

Therefore, the time constant of an RC circuit is a measure of how fast it charges or discharges.

RC Discharge Circuit Example

A capacitor is fully charged up to 10 volts. When the switch is first turned off, let's calculate the RC time constant, which is τ of the RC Discharge circuit below.

RC Discharge Circuit

The time constant τ is found using the formula t = R * c in seconds.

Therefore, the τ time constant is given as follows: T = R * C = 100k x 22uF = 2.2 seconds

a) How much will the voltage be along the capacitor at 0.7 time constants?

VC = 0.5 Vc at time constants of 0.7 ( 0.7 T ). Therefore, Vc = 0. 5×10 V = 5 V

b) How much will the voltage be along the capacitor after 1 time constant?

Vc = 0.37 Vc in 1 time constant ( 1T ). Therefore, Vc = 0. 37×10 V = 3.7 V

c) How long does it take for the capacitor to "completely empty" itself (equal to 5 time constants)

1 time constant ( 1T) = 2.2 seconds. Therefore, 5T = 5 x 2.2 = 11 seconds