Calculating Electric Charge: Find the Current in a Wire

[Colts]

Homework Statement

(a) The current through a wire is a steady 2.5 amps. How much current passes through it between t = 0 seconds and t = 4 × 10^-4 seconds?

For this one I thought it would be 2.5( 4 × 10^-4), but it says how much current and I thought current was a rate. So what does the question mean?

(b) The current through a wire is given by I(t) = I0e -at, where I0 = 2.5 amps and a = 6 × 103 s-1. How much electric charge passes through the wire between t = 0 seconds and t = 4 × 10-4 seconds?

This is the same way. Do I just plug t in?

Homework Equations

The Attempt at a Solution

 

[rude man]

Homework Statement

(a) The current through a wire is a steady 2.5 amps. How much current passes through it between t = 0 seconds and t = 4 × 10^-4 seconds?

For this one I thought it would be 2.5( 4 × 10^-4), but it says how much current and I thought current was a rate. So what does the question mean?

You're quite right. It should have asked for the charge, not the current. The current is 2.5A, no matter when.

(b) The current through a wire is given by I(t) = I0e -at, where I0 = 2.5 amps and a = 6 × 103 s-1. How much electric charge passes through the wire between t = 0 seconds and t = 4 × 10-4 seconds?

This is the same way. Do I just plug t in?
[/quote]

No. Charge is the integral of current. You need to integrate the current to get the charge.

Homework Equations

The Attempt at a Solution

[/QUOTE]

 

[Doc Al]

(a) The current through a wire is a steady 2.5 amps. How much current passes through it between t = 0 seconds and t = 4 × 10^-4 seconds?

For this one I thought it would be 2.5( 4 × 10^-4), but it says how much current and I thought current was a rate. So what does the question mean?

You are correct: Current is a rate. I would just treat it as a sloppily worded problem and assume they meant how much electric charge passes through it. (Just like in the second question.)

(b) The current through a wire is given by I(t) = I0e -at, where I0 = 2.5 amps and a = 6 × 103 s-1. How much electric charge passes through the wire between t = 0 seconds and t = 4 × 10-4 seconds?

This is the same way. Do I just plug t in?

The current isn't constant, so you need to be careful. Hint: Use a bit of calculus.