Formulas used in capacitor circuits

[influx]

http://photouploads.com/images/photo1igi.jpg

These formulas have been provided to me for use in RC circuits. However, they haven't been defined in the lecture notes. I know V_c = voltage across the capacitor, but isn't that what V_c(t) is as well? Is there any difference between the two?

Thanks

 

[NascentOxygen]

Vc is usually just an abbreviated way to write Vc(t)

though I'd say in this case your lecturer simply forgot to write the (t) after Vc

Can you draw two different circuits illustrating where these formulae apply?

 

[gfd43tg]

The hint from NO is that that formula is very specific and only applys to circuits that follow a very exact format. If your circuit is RC with some other components added (extra resistors, inductors, more capacitors) then you cannot use that formula. So be cautious when using it. If you have extra components, you must thevenize the circuit to take the format of the simple RC circuit.

Also, it appears they are assuming the capacitor is initially uncharged, hence Vo = 0 V. That is why it disappears in your second equation.

 

[psparky]

What NO and Maylis say is all true.

It takes a lot of practice to get good at these problems. Steady state vs transient...what's happening at t=0+...what's happening at 1 (RC)...what's happening at 5(RC), time constants if you will.

How all this relates to differential equations and laplace transform, also refers to bode plot...

How inductors and caps act like "shock absorbers" during transient. How inductors and caps short and open during steady state, yet inductors "stop/resist" current and capacitors "devour/accept" current at t=0+

How inductors release current the same way they received it, how caps release current the opposite way they received it like a battery.

Then you have how inductors and caps behave during AC. We tend to ignore transient in the AC world in colllege, yet we focus on transient of AC a lot more in the real world (large current draw with motor startup).

Lots and lots to learn...keep your mind open. Do not get tunnel vision.

Good luck!

 

[rezeew]

for sharing this image of the formulas used in capacitor circuits. I can confirm that Vc stands for the voltage across the capacitor, while Vc(t) represents the voltage across the capacitor at a specific time t. This notation is used to show that the voltage across the capacitor can change over time in a circuit. It is important to note that Vc and Vc(t) are not the same, as Vc(t) is a function of time, while Vc is the steady-state voltage across the capacitor. I hope this clarifies any confusion and helps you better understand these formulas.