| ADVANCED LESSON 18 | |
| LEARNING OBJECTIVES and Notes |
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| Capacitance 2 | |
| Charging a Capacitor | |
| Understand the charging and discharging of a capacitor in a CR circuit and the meaning of the time constant T=CR. If a circuit is set up as shown in the drawing, the rate of charge can be plotted on a graph by taking a reading of voltage across the capacitor at intervals of time. When the switch is closed,current starts to flow in the resistor and the capacitor starts to charge. The formula for the so called time constant is  Where T is in seconds (s), C is in Farads, and R is in ohms. Lets assume the resistor is 1 ohm and the capacitor is 1 Farad. Then T=CR T=1x1 T=1 second As the graph shows after 1 Time Constant with a 9v battery the capacitor has been charged to 5.7V (63%) After 2 time constants the charge on the capacitor = 7.8V (86%) After 3 time constants the charge on the capacitor = 8.6V (95%) After 4 time constants the charge on the capacitor =8.8V(98%) After 5 time constants the charge on the capacitor = 8.9V (99%) Notice that charging slows down with time. This is because as the capacitor charges up the PD across the resistor is reduced and this reduces the current flow and the rate of charge. So, The Time Constant of an RC circuit is the time taken to charge a capacitor to 63% of the supply voltage. |
 Example 1 Click "next step" to see the stages in the calculations  |
| Discharging a Capacitor This circuit is used to show how a charged capacitor discharges when shorted out via a resistor. When the switch is closed, current flows through the resistor and the voltage across the capacitor gets smaller. At first the drop in voltage is rapid because the voltage across the capacitor is high. As the voltage reduces, the rate of decline decreases, but by about 5 time constants the voltage across the capacitor is nearly zero. |
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Recall the dangers of stored charges on large or high voltage capacitors. Recall that large value resistors can be used to provide leakage paths for these stored charges.
As a safety precaution, a high value BLEED RESISTOR is placed across the capacitor. The bleed resistor allows the charge to slowly leak away without affecting the operation of the circuit. Bleed resistors are commonly used in high voltage power where considerable charges can build up across the smoothing capacitors. |
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| Capacitors in series and in parallel Understand and apply the formulae for calculating the combined values of capacitors in series and in parallel. As resistors can be connected in series and parallel to achieve a different value, the same applies to capacitors. The formulae are the revers of those used for resistance. Capacitors in series  Capacitors in parallel  Remember that the formulae can be used with any number of capacitors. This page happens to show 3, but for 5 capacitors the formula would be C total = C1+C2+C3+C4+C5 for capacitors in parallel |
 Click "next step" to see the stages in the calculations  Example 3 Click "next step" to see the stages in the calculations  |