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Postby TGTS0907129» Charge growth and decay in capacitor

Describe the growth and decay of charge in a capacitor

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When a steady voltage is introduced into a circuit containing only capacitance and resistance the change flow s into the capacitor rapidly at first. As the potential difference q/C between the plates of the capacitor rises, the rate of growth of change decreases until the transfer of electricity stop entirely when the voltage of electricity stop entirely when the voltage of the capacitor becomes equal to the potential V of the charging source. At every instant during the rise
                           


where, i is the instantaneous current and q is the instantaneous change. The resulting equation for the growth of charge is similar to that for the growth of current in the inductive circuit. The charge at any time t given by
                                    


The rate of flow of change, the current, is high initially and decreases exponentially,
                                   


When the switch is thrown quickly to position 2V becomes zero and the capacitor discharges exponentially. During the discharge the current reveres direction, and hence iR is negative.

In the charging of the capacitor energy was expended and stored in amount  1/2CV2. In the discharge this stored energy is dissipated as heat. If the resistance is sufficiently high so that all the energy has been dissipated by the time the capacitor is completely discharged, the simple exponential curve represents the manner of decay. If the resistance is so low that the energy is not all dissipated in this time, the remaining energy is not will be stored in the magnetic field of the connecting wires be stored in the magnetic field of the connecting wires and will maintain the current of self-inductance. This energy is then transferred to the capacitor, and it becomes charged oppositely from the original charge. The discharge continue until all the energy has been dissipated by the resistance.
 

By TGTT24071251 on 9/23/2015 10:33:57 PM
TGTS0907129 on 9/23/2015 5:12:33 AM
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