Time Constant

Resistor capacitor circuits do not exist in stable states continuously. There can be fluctuations in their condition due to changing voltage levels and input. This can be done by opening or closing the switch of a circuit. An RC circuit takes some time to respond to changes in voltage or input. This is because of the presence of resistors and capacitors. The rate at which the circuit changes from one stable state to another is determined by the time constant of the circuit. This time constant is the product of the resistance of the circuit in ohms and the capacitance of the circuit in farads. The Greek letter tau represents it.

Meaning of Time Constant

The meaning of the time constant of an RC circuit is the time required to charge the capacitor to 63.2% of the value through an applied DC voltage.

𝜏 =RC

Where R is circuit resistance and C is circuit capacitance

 Conversely, the period required to discharge a capacitor to about 36.8% of its value is also one time constant of the circuit. It is used in the following formulae to find out the voltage across the capacitor in relation to time

• When charging towards the applied voltage from zero voltage(V0) : V(t)=V0(1-e-t/𝜏)

Where 𝜏 is RC time constant

• Discharging towards zero voltage(V0) : V(t)=V0(e-t/𝜏)

The RC Time Constant

In an RC circuit, the resistance responds almost instantly to any change in voltage applied to the circuit. However, a resistor does not store energy. It is a passive device that dissipates energy in the form of heat energy. On the other hand, a capacitor can store energy in the form of an electrostatic field. It comprises two electrodes that are plates made of conducting material. An insulating material separates these plates. This material is dielectric and can store electrostatic energy.

The capacitor, unlike the resistor, cannot respond instantaneously to the changes in the voltage applied to the circuit. There will always be a short period of time immediately after the voltage is firstly applied for the circuit current and voltage across the capacitor to change state.This means that there will be a certain delay in the capacitor changing its stored energy within its electric field. This will hold true both for when the energy has to be increased and when the energy has to be decreased.

The amount of time required by a circuit to respond to changes is found to always be in multiples of the product of the resistance and the capacitance of the circuit. It is the product of ohms and farads written in seconds. The following equation expresses the current that is in the capacitor.

iC =C(dv/dt)

Here dv is the change in voltage and dt is the change in time.

Resistor Capacitor Circuit

If the circuit is shorted in a resistor-capacitor circuit, no current flows through it because it is not connected to the voltage supply. Once the circuit switch is turned on, a certain voltage is applied across the circuit. The moment the switch is turned on, the capacitor, which was fully discharged, acts as a short circuit because of the sudden change in the dv/dt condition.

Conclusion

The meaning of time constant is the time taken by the capacitor to be charged to about 63.2% of its full value through a resistor connected to it in series. RC time constant (𝜏) is the product of circuit resistance(R) and circuit capacitance(C).

𝜏 =RC

Conversely, time constant can also be defined as the time taken by a capacitor connected to a resistor in series to about 36.8% of its full value. It is an important value because it signifies the circuit’s growth rate or decay. The lower the value of the time constant of a circuit, the higher the rate of growth or decay of the circuit. And the higher the value of the time constant of a circuit, the lower the rate of growth or decay.