Part A After how many time constants does the current in Fig

Part A.)

After how many time constants does the current in Figure 21-38 in the textbook reach within 9% of its maximum value? (refer to picture)

Part B.)

After how many time constants does the current reach within 0.9% of its maximum value?

Part C.)

After how many time constants does the current reach within 9×10²% of its maximum value?

Solution

In a RC circuit charge as a function of time for chargin is given by

I=I_maxe^-t/T

a)

Given I=0.09I_max

=>0.09 = e^-t/T

-t/T =Ln(0.09)=-2.4

t=2.4T

so answer is 2.4 time constants

b)

Given I=0.009I_max

=>0.009=e^-t/T

t=4.7T

So answer is 4.7 time constants

c)

I=0.0009I_max

=>0.0009=e^-t/T

t=7T

So answer is 7 time constants