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Lesson 10-2 RC Time Constant

RC Time Constant

Before starting this module, you should be able to:

When you complete this module, you should be able to:

Describe the meaning of charging capacitor and discharging a capacitor.
Explain how AC current flows in a capacitor circuit, but with none flowing through the capacitor, itself.

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Describe the equation for determining the time constant of a series RC circuit.
Calculate the RC time constant of a circuit.
Explain the significance of the percentage value 63.2% in the process of charging a capacitor through a resistance.
Explain why a capacitor is considered fully charged at the end of 5 time constants.
Calculate the amount of voltage on a capacitor after it has charged a given number of time constants.
Explain the significance of the percentage value 63.2% in the process of discharging a capacitor through a resistance.
Explain why a capacitor is considered fully discharged at the end of 5 time constants.
Calculate the amount of voltage on a capacitor after it has discharged a given number of time constants.

RC Time Constant

The time constant of a series RC circuit is the product of the resistance value times the capacitance value: T = RC

where

T = time constant in seconds
R = resistance in ohms
C = capacitance in farads

The time constant for an RC circuit is nothing more than the product of R times C.

You will also find the Greek letter t (tau) used as the math symbol for time constant. For instance: t = RC

What is the time constant of a series RC circuit where R = 10 kW and C = 1 mF?

Ans: 10 ms

RC Charge Curve

This capacitor is begin charged from source Vs through resistor R.

A capacitor in a series RC circuit does not charge at a steady rate. Rather, the rate of charge is rapid at first, but slows considerably as it reaches full charge.

During each time constant, the capacitor charges 63.2% of the remaining distance to the maximum voltage level.

A capacitor is considered fully charged at the end of 5 time constants.

RC Charge Table

T	Vc
0	0
1	0.632 x Vs
2	0.865 x Vs
3	0.950 x Vs
4	0.981 x Vs
5	0.992 x Vs

This table shows how to calculate the voltage across a capacitor at the end of each time constant.

T = number of time constants that have passed.
Vc = voltage on the capacitor
Vs = voltage of the DC source

Vs = 12 V
R = 270 W
C = 100 nF

What is the time constant for this circuit?
What is the voltage across the capacitor after 2 time constants have passed?

Ans: T = 27 ms, Vc = 10.4 V

Part 1:

T = RC
T = 27 ms

Part 2:

After 2 time constants:

Vc = 0.865 x Vs
Vc = 0.865 x 12 V
Vc = 10.4 V

RC Discharge Curve

This capacitor is now begin discharged through resistor R. It was initially charged to the value of the source voltage, Vs.

A capacitor does not discharge at a steady rate. Rather, the rate of discharge is rapid at first, but slows considerably as the charge approaches zero.

During each time constant, the capacitor discharges 63.2% of the remaining distance to the minimum voltage level.

A capacitor is considered fully discharged at the end of 5 time constants.

RC Discharge Table

T	Vc
0	V_max
1	0.368 x V_max
2	0.135 x V_max
3	0.05 x V_max
4	0.019 x V_max
5	0.008 x V_max

This table shows how to calculate the voltage across a capacitor at the end of each time constant.

T = number of time constants that have passed.
V_max = the maximum, or starting, voltage on the capacitor (usually Vs)
Vc = capacitor voltage at the end of a given time constant

A capacitor has been initially charge to 100 V. What is the voltage across the capacitor at the end of 3 time constants if R = 10 kW and C = 1.2 mF?

Ans: 5 V

After discharging for 3 time constants::

Vc = 0.05 x V_max
Vc = 0.05 x 100 V
Vc = 5 V

Author and Content Provider: David L. Heiserman
Publisher: SweetHaven Publishing Services

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