Current electricity

Electricity and Magnetism Level 2

The current $I(t)$ flowing through a wire for $t \geq 0$ is given by $I(t) = 2 ^ { - t }$ .

Find the total charge that will flow through the wire.

The answer is 1.442.

1 solution

Abhinav Jha
Oct 18, 2016

. solve the integral

There are many continuous, monotonically decreasing functions that satisfy $I (t+1) = I (t) / 2$ . It need not just be of the form $2^{-t}$ .

Other examples are of the form $2 ^{ -t} \times 2^{ f(t) }$ where $f(t)$ is a continuous function that satisfies $f (t) = f(t+1)$ and $|f(t) | < 1$ for all points $t$ .

As such, can you make it clear that you're looking for $I (t) = 2 ^{ -t }$ ?

Calvin Lin Staff - 4 years, 7 months ago

SImply charge flowing in $dt$ is $dq$ and , $dq=i dt \implies q = \int_{0}^{\infty} 2^{-t}dt = (\ln 2)^{-1}$ , I don't think we need to find the functional relationship.

Aditya Narayan Sharma - 4 years, 7 months ago

Current electricity

The answer is 1.442.

1 solution

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