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

Answer:

Q=1.42 C

Explanation:

Given that

$I=I_oe^{\dfrac{-t}{\tau}}$

When t= 0 ,Io = 3 A

τ = Time constant = 0.5 s

$I=3e^{-\dfrac{t}{\tau}}$

We know that

$I=\dfrac{dQ}{dt}$

Q=Charge ,I =Current

Q = ∫I.dt

Given that

t= 0 to t= 3τ= 1.5 s

The charge Q

$Q=\int_{0}^{1.5}3e^{-\dfrac{t}{0.5}}dt$

Q=1.42 C

Therefore charge flow conductor will be 1.42 C.