Example Question #4 : Electricity And Magnetism
Which of the following is equal to the time constant of an RC circuit?
The definition of a time constant for an RC circuit is the product of resistance and charge:
This is defined as the time it takes the capacitor to reach a charge that is around 63% of the maximum charge. It is also the time it takes to discharge around 37% of the charge. This value is commonly used to determine the amount of charge a capacitor has or the amount of current flowing through the capacitor at any given time point.
Example Question #1 : Electric Circuits
Which of the following statements is false regarding capacitors?
I. A larger capacitor stores more energy
II. Capacitors connected in parallel have the same voltage drop
III. Increasing the distance between the two plates increases the capacitance
I and III
II and III
I and III
Recall the equation for potential energy in terms of capacitance:
According to the equation above, an increase in capacitance will lead to decrease in the amount of energy stored. This means that a larger capacitor will store less energy; therefore, statement I is false.
Any circuit elements connected in parallel will always have the same voltage drop. This applies to resistors, capacitors, and inductors. Statement II is true.
Remember that capacitance is defined as follows:
In this equation, is the area of the plates and is distance between the plates. Increasing will lead to a decrease in capacitance; therefore, statement III is false.
Example Question #2 : Electric Circuits
A capacitor has a stored charge of and a potential energy of . What is the voltage across the capacitor?
To solve this problem, you need to use the following two equations:
By substituting into the second equation you can write the change in potential energy in terms of voltage and charge.
Rearranging the previous equation will allow us to solve for the voltage.
Use the given values for stored potential energy and charge to solve for the voltage.