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

Answer:

Explanation:

Io = 4 A

τ = 0.60 s

The equation of current is given by

$I = I_{0}e^{\frac{-t}{\tau }}$

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

So, $\frac{dq}{dt} = I_{0}e^{\frac{-t}{\tau }}$

$\int_{0}^{q} dq = \int_{0}^{3}I_{0}e^{\frac{-t}{\tau }}dt$

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

q = 2.38 C