If you drive the RC circuit shown with an AC source V=V0cos(t), closing the swit

Question

If you drive the RC circuit shown with an AC source V=V0cos(t), closing the switch at t=0, the resulting current is:

I(t)= Vo*( R^2 + 1/(C^2^2))^(-1/2)*cos(t+)+ (Vo/R)*(1/(1+R^2C^2^2))*e^(-t/(RC))

with =arctan(1/RC).

You do not have to derive that formula! Instead, here are some questions about interpreting this result. (In all these questions, where we say “response”, I generally mean “the amplitude of current”)

1) What is the time constant for this circuit? (Can you just “spot it”? No calculation needed!) Briefly, how do you interpret it physically, what is it telling you? How would you make it longer?

2) How do you read off from that formula the “long time” response? (Again, no calculation needed, can you just “spot it”?) Describe this long term response in words, what is physically happening?

Explanation / Answer

1) Time constant means the time taken to change the initial value of circuit prameters like voltage or current by 63% in a transient condition. For Rc circuit the time constant T=RC .Now considering the discharge state or 0 volts voltage as initial value and V0Cost as final value

we apply final-initial voltage= (1-1/exp(T/t)) to get the required time to see the change physically for the circuit

that means V0Cost=(1-1/exp(T/RC)) will express the time required to change. Therefore, to make it longer we need to increase the required timeT.

b) Now transient response depends on the RC value of the circuit. To make the response long time we can increase the resistor value that means the required time of capacitor discharge from V0Cost to some low value will take more time in the second modified circuit.

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.