"A total charge of 9.0 mC passes through a wire in 3.5 seconds. What is the current in the wire? How many electrons pass through the cross-sectional area in 10.0 s? If the number of charges that pass through the cross-sectional area during the given time interval doubles, what is the resulting current?"

1) 0.00257 A

2) electrons

3) 0.00512 A

Explanation:

1)

A current is defined as the flow of charge through a conductor.

The intensity of current is calculated as:

(1)

where

q is the amount of charge passing through a certain point in the conductor

t is the time interval during which this charge passes

In the wire in this problem we have:

is the charge

is the time elapsed

Therefore, the current in the wire is:

2)

To find the total charge passing through a given point of the wire in a certain time, we re-arrange eq. (1):

where

I is the current

t is the time interval we are considering

In this problem we have:

I = 0.00257 A is the current in the wire

t = 10.0 s is the time we are considering

Therefore, the charge is:

We know that this charge q consists of N electrons, so we can write

where

is the charge of one electron

Solving for N, we find:

3)

In this problem, we are told that the number of charges that pass through the cross-sectional area during the given time interval doubles, so we have:

Therefore, the total charge through the point in the wire in a time of

t = 10.0 s

will be

And so, the current in this case will be

And we see that this current is twice the current we had in part 1), because the current is proportional to the number of charge carriers.

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