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Unformatted text preview: nitial charge on the capacitor is taken as q0 . Energy stored in a Capacitor The power delivered to the capacitor is the product of the capacitor voltage and current. p(t ) v(t )i (t ) v(t )C dv(t )
dv(t ) Cv(t )
dt The energy supplied to the capacitor will be integral of the power over time. t t t0 t0 e p(t )dt Cv(t ) v dv
dt Cvdv C v 2 v0 dt
v0 If the capacitor is initially discharged v0 0 , e 12
Cv . 2 61 EE1002 Introduction to Circuits and Systems Capacitances in series and parallel Capacitors when connected in parallel add up. Capacitors in series combine according to the same rule as for the resistors in parallel. When capacitors are in parallel, then the voltage across all of them will be same. i v i1
C3 v1 (t ) v2 (t ) v3 (t ) v(t ) The current in each capacitor will be dependent on the value of each capacitor. dv(t )
i2 (t ) C2 dt
i3 (t ) C3
dt i1 (t ) C1 From KCL, the total current entering into all the capacitors will be the sum of individual currents entering into the capacitors. i (t ) i1 (t ) i2 (t ) i3 (...
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- Winter '14