Homework 18 ECE201 Linear Circuit Analysis Due in class Friday October 7 2011 1 The configuration of an RC circuit is given below Its first order differential equation has the form dx dt x 0 where the time constant is 1 a Using KCL express the resulting differential equation in terms of iC t b What is the time constant from part a c Using the equation from part a and i C dV dt express the differential equation from part a in terms of VC t d What is the time constant from part c e Using KVL express the resulting differential equation in terms of Vc t f What is the time constant from part e g Using the equation from part e express the differential equation in terms of iC t h What is the time constant from part g i If VC 0 3V C 2F and R 4 then what is the voltage VC t at t 30 seconds j If VC 0 3V C 2F and R 4 then how much time does it take until the voltage across the capacitor is reduced by about 37 k If VC 0 3V C 2F and R 4 then how much time does it take until the voltage across the capacitor is reduced by about 74 l If VC 0 3V and C 2F then what would be the value of R such that it would take 100 seconds for the voltage across C to reduce by about 37 m If VC 0 3V C 2F and R 4 plot charge Q t on the capacitor for 0 t 3 n If VC 0 3V C 2F and R 4 plot power Pabsorbed in the resistor for 0 t 3 2 In the RC circuit below the voltage source is V t 5u t where u t is the step function a Determine the effective resistance of this RC circuit or the resistance seen by the capacitor after shorting the independent voltage source b Determine the time constant of this RC circuit c Determine VC on the capacitor at t 0 d Determine VC on the capacitor at t 0 e Determine iC on the capacitor at t 0 f Determine iC on the capacitor at t 0 g Determine the charge Q on the capacitor at t RC seconds h Determine the charge Q on the capacitor at t 4RC seconds 3 In the RL circuit below determine the following symbolically a What is the effective resistance of this RL circuit b What is the effective inductance of this RL circuit c What is the time constant d If i 0 i0 then what is the initial current passing through the 12L inductor e If i 0 i0 then what is the initial current passing through the 6L inductor f If i 0 i0 then what is the initial current passing through the 2L inductor g If i 0 i0 then what is Vout t h If i 0 i0 then what is i t
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