Considering the RC Network shown in Figure , we can use KCL to write Equation (). R C Vo(t) Figure Source-free RC Network C ., dv o ( t ) v o ( t ) + =0 dt R () dv o ( t ) v o ( t ) + =0 dt CR If Vm is the initial voltage across the capacitor, then the solution to Equation () is v 0 (t ) = Vm e where t − CR () CR is the time constant Equation () represents the voltage across a discharging capacitor. To obtain the voltage across a charging capacitor, let us consider Figure. | Attia John Okyere. Transient Analysis. Electronics and Circuit Analysis using MATLAB. Ed. John Okyere Attia Boca Raton CRC Press LLC 1999 1999 by CRC PRESS LLC CHAPTER FIVE TRANSIENT ANALYSIS RC NETWORK Considering the RC Network shown in Figure we can use KCL to write Equation . dv t v t C - 0 dt R . dv- t v- t 0 dt CR If Vm is the initial voltage across the capacitor then the solution to Equation is t 1 vo t Vne 1CR J where CR is the time constant Equation represents the voltage across a discharging capacitor. To obtain the voltage across a charging capacitor let us consider Figure . 1999 CRC Press LLC R AAÆ Vs Vo t Figure Charging of a Capacitor Using KCL we get Cdvo t vo t - Vs 0 dt R If the capacitor is initially uncharged that is v0 t 0 at t 0 the solution to Equation is given as -1 v0 t VS 1 - e 1CR Vs 7 Examples and illustrate the use of MATLAB for solving problems related to RC Network. Example Assume that for Figure C 10 pF use MATLAB to plot the voltage across the capacitor if R is equal to a kQ b 10 kQ and c kQ. Solution MATLAB Script Charging of an RC circuit c 10e-6 r1 1e3 1999 CRC Press .
