The current supplied by a battery slowly decreases as the battery runs down. Suppose that the current as a function of time is I
= ( 0.860 A
 ) e−t/6hr
 .What is the total number of electrons transported from the positive electrode to the negative electrode by the charge escalator from the time the battery is first used until it is completely dead?

To find the total number of electrons transported from the positive electrode to the negative electrode, we need to calculate the total charge \( Q \) transported by the current over the time period from when the battery is first used until it is completely dead.

The current is given by:

\[
I(t) = (0.860 \, \text{A}) \, e^{-t/6 \, \text{hr}}
\]

### Step 1: Express Current in SI Units
Since the current is in amperes, and time is in hours, we need to convert time into seconds to use standard SI units. The time constant here is \( 6 \, \text{hr} = 6 \times 3600 \, \text{s} = 21600 \, \text{s} \).

Thus, the current equation becomes:

\[
I(t) = (0.860 \, \text{A}) \, e^{-t/21600 \, \text{s}}
\]

### Step 2: Total Charge Transported
The total charge transported \( Q \) is the integral of the current

The current supplied by a battery slowly decreases as the battery runs down. Suppose that the current as a function of time is I = (0.860 A) e^(-t/6 hr). What is the total number of electrons transported from the positive electrode to the negative electrode by the charge escalator from the time the battery is first used until it is completely dead?

Learn how to calculate the total number of electrons transported from the positive to the negative electrode in a battery with an exponentially decaying current, I(t) = 0.860 A e^(-t/21600 s). This solution covers exponential decay, integration, and charge calculation. Suitable for undergraduate physics and math students.

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