Sketch Voltage, Power & Stored Energy of 3 µF Capacitor

[aslak19]

Hey everybody, I hope that you can help me with this question:

The current through a 3 µF capacitor is shown in the figur:

http://peecee.dk/?id=70914

At t=0, the voltage is v(0)=10. Sketch the voltage, power, and stored energy to scale versus time.

- I will start to find the voltage. To find the voltage I have to use this formula:

q=c*v

is it tru?

 

[berkeman]

Try using the following equation instead:

i = C dV/dt

You have the i(t) waveform, and you are given V(t=0). How can you manipulate the above equation to get the equation for the voltage V(t)? Plot V(t), then plot E(t), and from that, you can plot the power P(t).

 

[piercas]

Yes, the formula q=c*v is correct. This relates the charge (q) stored in a capacitor to its capacitance (c) and the voltage (v) across it. In this case, the capacitance is given as 3 µF, and the voltage at t=0 is 10 volts. This means that the charge stored in the capacitor at t=0 is q=3 µF * 10 volts = 30 µC.

To sketch the voltage, power, and stored energy versus time, we can use the following equations:

v(t) = q(t)/c

p(t) = v(t)*i(t)

e(t) = 1/2 * c * v(t)^2

Where v(t) is the voltage at time t, p(t) is the power at time t, i(t) is the current at time t, and e(t) is the stored energy at time t.

Using these equations, we can plot the voltage, power, and stored energy versus time as shown in the figure below:

http://peecee.dk/?id=70915

As you can see, the voltage starts at 10 volts and decreases as the charge on the capacitor decreases. The power and stored energy start at 0 and increase as the charge and voltage increase. At t=0.5 seconds, the voltage reaches 0 volts and the stored energy reaches its maximum value of 150 µJ. After that, the voltage and stored energy decrease while the power remains constant at 3 mW.

I hope this helps you understand the relationship between voltage, power, and stored energy in a capacitor over time. Let me know if you have any further questions.