The electric current through a wire varies with time as , where A and A s. The amount of electric charge crossed through a section of the wire in 20 s is:

Question

The electric current through a wire varies with time as , where  A and  A s. The amount of electric charge crossed through a section of the wire in 20 s is:

Canvas Classes · Accepted Answer

🧠 Same Idea — Integrate When Current Depends on Time

Look at the form of the current:  with  A and . It is changing with time, so charge is not  — it is the integral of current over time.

The first move: write  and plug in. Notice that  is linear in  here too, so the average-current shortcut from CURR-001 also works. I will show both.

🗺️ Working It Out

By direct integration:

At : .
At : everything is zero.

So .

⚡ The Smart Move — Mean of End-Values

Because  is linear in :

Then . D

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More questions from this chapter