Question

A conductor carries a current that is decreasing exponentially with time. The current is modeled as ????=????0????−????/???? , where ????0=3.00A is the current at time ????=0.00s and ????=0.50s is the time constant. How much charge flows through the conductor between ????=0.00s and ????=3???? ?

Answer 1

Q=1.42 C

Step-by-step explanation:

Given that

`I=I_oe^{(-t)/(\tau)}`

When t= 0 ,Io = 3 A

τ = Time constant = 0.5 s

`I=3e^{-(t)/(\tau)}`

We know that

`I=(dQ)/(dt)`

Q=Charge ,I =Current

Q = ∫I.dt

Given that

t= 0 to t= 3τ= 1.5 s

The charge Q

`Q=\int_(0)^(1.5)3e^{-(t)/(0.5)}dt`

Q=1.42 C

Therefore charge flow conductor will be 1.42 C.