Calculating Capacitor Charge & Voltage: A Problem

In summary, the conversation discusses finding the charge and voltage on a 0.25uF capacitor at specific times, and also calculating the energy stored in the capacitor by a given current. The method involves finding the area under the given current graph up to the specified time, and then dividing the result by the capacitance to find the voltage. The energy stored can be calculated using the final voltage of the capacitor.
  • #1
tehipwn
16
0

Homework Statement


The current shown below is applied to a 0.25uF capacitor. The initial voltage on the capacitor is zero.
(a) Find the charge on the capacitor at t = 30us.
(b) Find the voltage on the capacitor at t = 50us.
(c) How much energy is stored in the capacitor by this current?

http://img296.imageshack.us/img296/1800/currentgraphyk8.png

http://img513.imageshack.us/img513/302/problemdescriptionqw0.png

Thank you very much for any help you offer. This has had me bogged down for a couple hours now and I just want to understand how they got those answers in the back of the book.
 

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  • #2


There is no need to "work backwards."

The total charge accumulated at time t is the integral of the current up to time t. So find the area underneath the curve up to t = 30 us in order to find q(30 us). You should get 1.25 uC.
 
  • #3


Finding the voltage requires exactly the same procedure as I described above for the charge. (After all, the voltage is simply proporational to the charge accumulated). You can see that from the equation you've been given. You just have to compute the integral up until t = 50 us, and then divide the answer by C.
 
  • #4


I interpret part c to be asking how much energy is stored in the process of charging up this capacitor using this current (i.e., at the end of it all, how much energy is stored)? Therefore, all you have to do is calculate the energy based on the capacitor's final voltage.
 
  • #5


Thank you very much for your help. It all works out now.
 

FAQ: Calculating Capacitor Charge & Voltage: A Problem

How do you calculate the charge on a capacitor?

To calculate the charge on a capacitor, you can use the formula Q = CV, where Q is the charge in coulombs, C is the capacitance in farads, and V is the voltage in volts. Alternatively, you can also use the formula Q = It, where I is the current in amperes and t is the time in seconds.

What is the relationship between capacitance and charge?

The capacitance of a capacitor is directly proportional to the charge on the capacitor. This means that as the capacitance increases, the charge on the capacitor also increases, and vice versa.

How do you calculate the voltage on a capacitor?

The voltage on a capacitor can be calculated using the formula V = Q/C, where V is the voltage in volts, Q is the charge in coulombs, and C is the capacitance in farads. This formula can also be rearranged to find the capacitance or the charge, depending on which values are known.

What factors affect the charge and voltage on a capacitor?

The charge and voltage on a capacitor are affected by the capacitance, the current flowing through the capacitor, and the time the capacitor has been charging. The type of dielectric material in the capacitor can also affect its capacitance and therefore its charge and voltage.

How does a capacitor discharge?

A capacitor discharges when the stored charge on the plates is released, usually due to a decrease in voltage across the capacitor. This can happen when the circuit is turned off, or when the capacitor is connected to a circuit with a lower voltage. The rate of discharge is determined by the capacitance and the resistance in the circuit.

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