| Physics Graphs: Charging a Capacitor |
The following graph of charge vs. time represents the growth of charge (Q) on a capacitor while it is attached to a voltage source. The dotted asymptote represents the capacitor's final, or maximum allowed, charge, Q f which equals the product of the capacitor's capacitance (C) and the applied voltage (  ). When a capacitor is placed in a circuit with a resistor, it is call an RC circuit. For every RC circuit there is a specific value known at its "RC time constant" which is equivalent to the product of the resistance in the circuit (R) the capacitance of the capacitor (C). When a tangent line is drawn at the beginning of a capacitor's charging curve, it will intercept the asymptote representing the capacitor's final charge at t = RC. Some units that you need to know are:
- charge (Q) is measured in coulombs
- resistance (R) is measured in ohms
- emf (
 ) is measured in volts
- capacitance (C) is measured in farads
- time (t) is measured in seconds
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General Questions |
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If the voltage source,  , equals 120 volts and the capacitor, C, equals 100 microfarads, what is the maximum charge this capacitor can hold once the switch is closed?
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If the resistor present in our circuit is 500 kilo-ohms, what is circuit's RC time constant? |
The formula used to calculate the amount of charge present on a charging capacitor at any time t, Q(t) is:
(a) Use this formula to determine how much charge will be on the capacitor after the switch has been closed for 1 RC time constant. Express your answer to 4 significant digits. (b) What percent of the final maximum charge does this represent? |
(a) How much charge will be on the capacitor after the switch has been closed for 5 minutes? Express your answer to 4 significant digits. (b) What percent of the final maximum charge does this represent? |
(a) How much charge will be on the capacitor after the switch has been closed for 10 minutes? Express your answer to 4 significant digits. (b) What percent of the final maximum charge does this represent? |
| Use your previous three answers to describe the behavior of the graph as the time spent charging the capacitor continues to increase. |
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C Colwell
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