Question

The current supplied by a battery as a function of time is What is the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead? (e = 1.60 × 10-19 C)

Answer 1

Complete Question

The current supplied by a battery as a function of time is I(t) = (0.88 A) e^(-(t * 6 hr)). What is the total number of electrons transported from the positive electrode to the negative electrode from the time the battery is first used until it is essentially dead?

Answer:

The total number of electrons transported is $n=2.54*10^{14}\ electrons$

Explanation:

Charge is generally expressed as

           $q = \int\limits^{\infty}_0 {I} \, dt$

Where I is the current and it is given as

         $I = (0.88A) e^{{ -t *6 hr} } = (0.88A) e^{-21600t} }$

Substituting into equation above d

        $q = \int\limits^{\infty}_0 {0.88 e^{-21600t}} \, dt$

           $q = 0.88[-\frac{e^{-21600t}}{21600} ]\left \ {{\infty} \atop {0}} \right.$

          $q = - \frac{0.88}{21600} [-1]$

           $q = 4.074*10^{-5}C$

   This charge can also be expressed as

            $q = n *e$

Where is the number of electron

Making n the subject

             $n = \frac{q}{e}$

                $= \frac{4.074*10^{-5}}{1.60*10^{-19}}$

               $=2.54*10^{14}\ electrons$