## Question

###### 3. Voltage in RC Circuit For the circuit shown determine the expression for the voltage across...

3. Voltage in RC Circuit For the circuit shown determine the expression for the voltage across the 1.5 k2 resistor Vy() for 10, then use this expression to find the vx in (V) at time? - 25 ms. Note that the switch opens at: -0. 1kΩ 10 V 1.5 kn 333 F 1=0

## Answers

Solhi- niven circuit I kn + 1.ska lov 333 xf ta Vt=0 now switch was closed before find initial voltage t=0, so let capacitor, which across us balgaves as open circuit for stedy state in dc. iie Iku + 1+ lska Vc (0) { بیاد W from voltage division rule 10 X 1.5 km Vcco-) - 6V (1 km. int 1.5kn) we that know now voltage across Capacitor is continuous i.e. it can not change instantaneouse y. hence Veco-) Vc (ot) = 6V will how look like after switch is circuit opened,+ + 1.5kn Vu 333MF Vc V(ot) = 60 how above circuit is standard RC circuit and for standard RC circuit voltage across capacitor (same as vu) is given the V (00) + (vecot) – Velos) e (t) = C where Vc() = voltage across capacitor when too Vecos) will be zero, o, because in there our case is no source in the circuit hence Vcco) = vetot) initial roltage on capacitor Vecot) = in our case z = time constant of the circuit 7 = RC in our case T= (isxio3) * (333x1000) z = 0.4995 seconds Hence Vc(t) = u(t)= 0 + (0-0)2-44999 - 2.002t or Vy(t) = 6 e VoltsHence -2-002t 6 e Valt) volts tzo Ans value of Un at t = 25 ms now - 2.002X25X10-3 6.e ur = Vu 5, 7071 Volts hence value of Un at t-asms is 5.7071 volts

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