Question

Charge is moving through a wire. An amount of charge Q moves past a particular spot in the wire in an amount of time t to produce a current I.
What happens to the magnitude of the current when it takes five times as long for the same amount of charge is moved past that point in the wire at a steady rate?

Answer 1

We will apply the concept related to the current change given in the same problem. We will divide both currents into two states: the new current and the old current. As the current is the change of the load in a certain time, we will have that the old current is,

$I_{old} = \frac{dq}{dt}$

If it takes 5 times more time, then we will have the new current is,

$I_{new} = \frac{dq}{5dt}$

$I_{new} = \frac{1}{5}(\frac{dq}{dt})$

Replacing the given value of the old current we will have to,

$I_{new} = \frac{I_{old}}{5}$

Therefore the new current will be $\frac{1}{5}$ the old current.