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Unformatted text preview: ngle capacitance. Discharge of a capacitor through a resistance t 0 vC Prior to t=0, the capacitor was charged to an initial voltage Vi. Then at t=0, the switch is closed and the capacitor discharges through the resistance. 70 EE1002 Introduction to Circuits and Systems According to KCL, the current entering in to the capacitor equals to the current into the resistor: dvc (t ) vc (t ) 0
dt
R dvc (t ) vc (t ) 0
RC
dt C To find the value of the capacitor voltage we need to solve a first order differential equation. The solution to the first order differential should be a function which has the same form as its first derivative. As the first derivative of an exponential function is also an exponential function, it could be a possible solution. Let us try the function vc (t ) Ke st . With this function, the differential equation will be RCKse st Ke st 0 . Solving for s, we obtain s t
1 and solution would be vc (t ) Ke RC . RC For the complete solution, we need to find out the value of K. We know that the voltage across the capacitor cannot change instantaneously. Hence, the voltage immediately after switch the cl...
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