Answer:
Iin(t) =1.3 × (-0.8/1.56) e^-t/1.56 A
Step-by-step explanation:
In physics, the determination of the term " natural response" simply means that we want to know what happens in a circuit when the value of t = 0, that is to say after the circuit has been disconnected. Hence, the value of the voltage and the current can then be determined or Calculated;
For the the natural response of i in(t) we will be using the formula below;
I(t) = Vo × t/ R = Vo/R × e^-t/h.
Where h = 1/RC = time constant.
For t= 0^- = 0.8 × 1= 0.8 V.
1/Ctotal = 1/ 2 + 1/3 = 6/5
For t = 0^+;
h =( 0.8 + 0.5) × 6/5 = 1.56 seconds.
Hence, we will have;
Vin(t) = 0.8 × e^-t/1.56.
Iin(t) =1.3 × (-0.8/1.56) e^-t/1.56