How to calculate the current in a discharge circuit after a certain time?

[smileandbehappy]

Hi, I have been set a sheet of questions for homework and there are two which I cannot do. Any help you could give would be greatly appretiated.

1)

The time constant "t" of the discharge of a capacitance C through a resistacne R is given by: t = RC.

Show that the unity of quantity RC is seconds.

I have tried doing this but keep getting into cycles of inputting equations into it and just going around in circles.

2) This is a two part question and I have done the first part.

Circuit diagram showing: 6V potential difference, 4700*10^-6F capacitor, 5.6*10^-3 ohm resistor resistor.

a) Show that the initial value of the discharge current is about 1mA

I = V/R

I = 6/(5.6*10^-3)

I = 1.071*10^-3A

b) The time constant RC of the discharge circuit is about 26s.


Calculate the current in the discharge circuit after the switch has been fora time equal to RC.

I don't have a clue how to do this!

 

[Hootenanny]

Welcome to the Forums,

1)I have tried doing this but keep getting into cycles of inputting equations into it and just going around in circles.

Okay, start with the basic equations for capacitance and resistance;

$$R = \frac{V}{I}$$

$$C = \frac{Q}{V}$$

Now using the fact that current is the rate of flow of charge ($I = \frac{Q}{t}$) can you eliminate the current (I) from the first equation?

2) This is a two part question and I have done the first part.
I don't have a clue how to do this!

Do you know the definition of the time constant?

 

[smileandbehappy]

"Do you know the definition of the time constant?"

No.

 

[Hootenanny]

"Do you know the definition of the time constant?"

No.

Okay, do you know any equations involving the time constant (besides t = RC)?

 

[smileandbehappy]

"Okay, do you know any equations involving the time constant (besides t = RC)?"

No sorry - t=RC is the only one given in the question.

 

[Hootenanny]

"Okay, do you know any equations involving the time constant (besides t = RC)?"

No sorry - t=RC is the only one given in the question.

Okay, well in this case the equation you need to know is;

$$I = I_{0}e^{\frac{-t}{RC}}$$

Where I is the current at time t and I₀is the intial current value. Has your tutor not given you this information?

 

[smileandbehappy]

Okay, well in this case the equation you need to know is;

$$I = I_{0}e^{\frac{-t}{RC}}$$

Where I is the current at time t and I₀is the intial current value. Has your tutor not given you this information?

No. I have never been shown this equation beofre either. Thanks for all your help, but I think it would be best if I went and asked tomorrow, because I think he may have made a mistake.

 

[Hootenanny]

No. I have never been shown this equation beofre either. Thanks for all your help, but I think it would be best if I went and asked tomorrow, because I think he may have made a mistake.

No problem. Have you any thoughts on the first problem?