Capacitor Charging and Discharging in DC Circuits PDF

The charge and discharge of a capacitor When a voltage is placed across the capacitor the potential cannot rise to the applied value instantaneously. As the charge on the terminals builds up to its final value it tends to repel the addition of further charge. The rate at which a capacitor can be c...

The charge and discharge of a capacitor When a voltage is placed across the capacitor the potential cannot rise to the applied value instantaneously. As the charge on the terminals builds up to its final value it tends to repel the addition of further charge. The rate at which a capacitor can be charged or discharged depends on: (a) the capacitance of the capacitor and (b) the resistance of the circuit through which it is being charged or is discharging. This fact makes the capacitor a very useful if not vital component in the timing circuits of many devices from clocks to computers. During charging electrons flow from the negative terminal of the power supply to one plate of the capacitor and from the other plate to the positive terminal of the power supply. When the switch is closed, and charging starts, the rate of flow of charge is large (i.e. a big current) and this decreases as time goes by and the plates become more charged so "resisting" any further charging. You should realise that the addition of a resistor in the circuit in series with the capacitor ONLY affects the TIME it takes for the capacitor to become fully charge and NOT the EVENTUAL POTENTIAL DIFFERENCE ACROSS IT – this is always the same and equal to the potential difference across the supply. The time constant The time that it takes the potential difference across the capacitor to fall to 1/e (37%) of its original value is called the time constant for the circuit. If a capacitor C is discharged through a resistance R then the time constant is equal to RC. You can see that the time constant is independent of the initial voltage and this makes it a very useful quantity when using capacitors in timing circuits. The voltage falls to 37% of the original value in RC seconds and falls to 14% (37% of 37%) in 2RC s. Discharging a capacitor When t = RC, V = V o /e = 0.37 V o and the product RC is known as the time constant for the circuit. The bigger the value of RC the slower the rate at which the capacitor discharges. The value of C can be found from this discharge curve if R is known. Charging a capacitor As the capacitor charges the charging current decreases since the potential across the resistance decreases as the potential across the capacitor increases. The area below the current-time curve in both charging and discharging represents the total charge held by the capacitor. The energy stored in capacitor The energy stored in a capacitor is given by the equation: Since the energy supplied by a power source is E = QV this means that capacitors store half the energy supplied to them (the rest is lost as heat in the wires and the power source).