Capacitor Charging Equation The transient behavior of a circuit with a battery, a resistor and a capacitor is governed by Ohm's law, the voltage law and the definition of capacitance. Development of the capacitor charging relationship requires calculus methods and involves a differential equation. For continuously varying charge the current is defined by a derivative This kind of differential equation has a general solution of the form: and the detailed solution is formed by substitution of the general solution and forcing it to fit the boundary conditions of this problem. The result is Charging capacitor Capacitor discharge
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DC Circuits

Capacitor Concepts

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Capacitor Discharge Calculation

For circuit parameters:
 R = Ω, V0 = V

 C = μF, RC = s = time constant. This circuit will have a maximum current of Imax = A
just after the switch is closed.
 The charge will start at its maximum value Qmax= μC.
 At time t = s= RC
 the current is = Imax = A,
 the capacitor voltage is = V0 = V,
 and the charge on the capacitor is = Qmax = μC

 Capacitor discharge derivation Capacitor charging discussion
Index

DC Circuits

Capacitor Concepts

 HyperPhysics***** Electricity and Magnetism R Nave
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