20.4

Charging a Capacitor

Student Notes

With this simulation, you can investigate an RC circuit, in which a resistor and capacitor are connected in series to a 10 volt battery. Two graphs are shown. The top graph displays the potential difference across the capacitor (i.e., the capacitor voltage) as a function of time. The bottom graph displays the current in the circuit as a function of time - this is the current through the resistor. Note that the time readout is reset whenever you press the Charge/Discharge button.
Here are some things to try to see if you fully understand the concepts. If possible, predict what you think will happen and then make the changes to see if you are correct. What is the maximum possible value of the capacitor voltage? What is the maximum possible value of the current in the circuit? How should you set the values of R and C to maximize the time constant? If the resistance in the circuit is increased, what happens to the maximum current? If the resistance is changed, how does this affect the time it takes to charge the capacitor to a given voltage? If the capacitance is increased, what happens to the time it takes to charge the capacitor to a given voltage? Does changing the capacitance affect the maximum current? If the capacitor starts off uncharged, and takes a time T to reach 2 volts, how much more time does it take to reach 4 volts? Is this additional time equal to T, less than T, or more than T? Why is this?

Self-test

The time constant for an RC circuit is R x C, the product of the resistance and capacitance. What does the time constant measure? In this simulation the battery voltage is 10 volts. When the capacitor voltage is 6 volts, what is the voltage across the resistor? Does Kirchoff's loop rule apply to this circuit? While the capacitor is charging, you can press the "Discharge the capacitor" button. What does this do to the sign of the current? Why is this? In DC circuits that involve only resistors and batteries, the current does not change with time. By adding a capacitor, as we have done here, the current does change with time. Why is this? How does the current change as time passes?

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