Question

The battery for a certain cell phone is rated at$\mathbf{3}\mathbf{.}\mathbf{70}\mathbf{}\mathbf{V}$.According to the manufacturer it can produce$\mathbf{3}\mathbf{.}\mathbf{15}\mathbf{\times }{\mathbf{10}}^{\mathbf{4}}\mathbf{}\mathbf{J}$of electrical energy, enough for $\mathbf{2}\mathbf{.}\mathbf{25}\mathbf{}\mathbf{h}$of operation, before needing to be recharged. Find the average current that this cell phone draws when turned on.

Short answer

The average current cell phone draws when turn on is$0.45\mathrm{A}$.

Step-by-step solution

Concept/Significance of average current.

Time-averaged current is the total amount of charge passing through a conductor in a time interval.

${\mathbf{I}}_{\mathbf{avg}}\mathbf{=}\frac{\mathbf{∆}\mathbf{q}}{\mathbf{∆}\mathbf{t}}$

Determination of the average current that this cell phone draws when turned on 

The average power of the battery is given by,

$P=\frac{E}{t}$

Here, E is the electric energy and t is the time

Substitute all the values in the above equation.

$$\begin{gathered} P=\frac{3.15\times {10}^4\mathrm{J}}{5.25\mathrm{h}\left(3600\mathrm{s}/\mathrm{h}\right)} \\ =1.66\mathrm{W} \end{gathered}$$

The average current is given by,

$I=\frac{P}{V}$

Here, P is the Power and V is the battery of the phone.

Substitute all the values in the above,

$$\begin{gathered} I=\frac{1.66\mathrm{W}}{3.70\mathrm{V}} \\ =0.45\mathrm{A} \end{gathered}$$

Thus, the average current cell phone draws when turn on is$0.45\mathrm{A}$.