The switch has been in position a for a long time. At t= 0, it moves to position b. Calculate i() for all t> 0. Take vs = 7o va t= 06ΩVs24 V (+3Ω2 FThe value of (1) for all t> 0 ise-0.25t A.

This circuit is an RC circuit. When the switch is at a fro a long time the capacitor will become open as the circuit reaches a steady-state. This will allow us to calculate V(0). When the switch is t b it will again reach a steady-state and we will be able to calculate V∞ . The equation governing the current through a capacitor circuit is given by, i(t)=CdVc(t)dt Capacitor voltage will be given by, VC(t)=VC(∞)+(VC0-VC∞)e-tτ Here τ is called RC time constant and is given by, τ=ReqC Here Req is the equivalent resistance and C total capacitance of the circuit. From the given data we can say, 1τ=0.25τ=4 When the switch is at a for a long time the circuit will reach steady-state and capacitor will become open then the circuit becomes as shown in figure (1), Now voltage will be given by, V(0)=(70 V)(3Ω6Ω+3Ω)=23.33 VNow the switch is moved to b and the circuit will reach steady-state. The circuit will then become as shown in figure (2), Now the voltage will be, VC(∞)=(24 V)(3 Ω3Ω+6Ω)=8 VThe voltage will now be given by, VC(t) =VC(∞)+(VC(0)-VC(∞))e-tτ=(8 V)+(23.33 V-8 V)e-t4=8+15.33e-0.25t V Now current will be given by, i(t)=CdVc(t)dt=(2 F) ddt (8+15.33e-0.25t) =2 (15.33 (-0.25) e-0.25t)=-7.665 e-0.25t Ai(t)=-7.665 e-0.25t AThus for all t>0, the current will be given by, i(t)=-7.665 e-0.25t A

Answered: The switch has been in position a for a…

The switch has been in position a for a long time. At t= 0, it moves to position b. Calculate (t for all t> 0. Take Vs= 70 V a t= 0 6Ω b Vs 24 V (+ - 2F The value of (t) for all t> 0 is e-0.25t a.