Question

The current through a wire depends on time as i = 10 + 10t +30t2. The charge crossed through a section of the wire in 10 s will be

Answer 1

$I = 10 + 10t + 30 t^2$

The rate of flow of charge is known as current.

Let the charge be q.

Hence,

$I = \frac{\delta q}{\delta t}$

$\delta q = I \delta t$

Doing the integration:

$q = 10t + 5 t^2 + 10 t^3$

Plug t = 10 in the above equation.

$q = 10 \times 10 + 5 \times 10^2 + 10 \times 10^3$

$q = 100 + 500 + 10000$

q = 10600 Coulombs

Hence, the charge crossed through a section of wire is: q = 10600 Coulombs