Lets have a look at the formula , of transient current

The things to be noted here that , the term RC remain constant during all operation and mathematical values.

The RC time constant, also called tau,

The time constant (in seconds) of an RC circuit, is equal to the product of the circuit resistance (in ohms) and the circuit capacitance (in farads), i.e.

The time constant is a measure that much time will be taken by a capacitor to charge . The larger the value of RC is , the larger time is required to charge the capacitor .

So physically speaking one RC constant is the time taken by current signal to decay by approximately 36.8 % of its original value

Example : RC constant

For the following capacitor

 

a. Sketch the current graph for following Situation

0.25
0.5
0.75
1
1.5
3

b. Find the voltage a 3 RC constant

Solution

 

 

 

X axis = Time

Y Axis = I(t)

b. Find current at 3 RC time constant

At three RC constant we have current value as 0.000100 Ampere

Finding voltage = V= IR

= 0.000100 X 15000

1.5 V

Transient Voltages

A RC circuit now consists of a resistor and capacitor . Hence it means at a particular time instant the total voltage in a circuit will be equal to the voltage in the resistor and capacitor

 

Hence total voltage in a circuit is

E = VR(t)+VC(t) …. Eq A

We know that V

Putting the value of VR(t) to Eq A

 

For the following Circuit solve.

a) Sketch the graph of Vc(t) and VR(t)

· 0s

· 0.05s

· 0.1s

· 0.2s

· 0.5s

· 0.8s

b) Verify KVL at t=0.5 s

Solving for Capacitor

 

 

 

Solving for Resistor

 

 

 

Solving KVL at 0.5s

E = VR(t)+VC(t) at 0.5 s

20V= 18.35V +1.64V

20V= 19.99V