Question

A conductor carries a current that is decreasing exponentially with time. The current is modeled as I = I0e−t/τ,where I0= 4.00 A is the current at time t = 0.00 s and τ = 0.60 s is the time constant. How much charge flows through the conductor between t = 0.00 s and t = 3.00 s?

Answer 1

Step-by-step explanation:

Io = 4 A

τ = 0.60 s

The equation of current is given by

`I = I_(0)e^{(-t)/(\tau )}`

Current is defined as the rate of charge flows through the conductor

So,
`(dq)/(dt) = I_(0)e^{(-t)/(\tau )}`

`\int_(0)^(q) dq = \int_(0)^(3)I_(0)e^{(-t)/(\tau )}dt`

`q = -4\tau \left ( e^{-(t)/(\tau )} \right )_(0)^(3)`

q = 2.38 C