Question

a cell phone battery holds a maximum charge of 1.420 ah. how long will it take a charger to fully charge the battery if it starts with zero charge and is charged at a constant rate of 900.0 ma?
47 minutes, 12 seconds
two hours
94 minutes, 41 seconds
24 minutes, 31 seconds

Explanation:

Step1: Convert capacity to mAh

The battery capacity is $1.420\ \text{Ah}$. Since $1\ \text{Ah}= 1000\ \text{mAh}$, the capacity $Q = 1.420\times1000=1420\ \text{mAh}$.

Step2: Use the formula $t=\frac{Q}{I}$

The charging - current $I = 900.0\ \text{mA}$. Using the formula $t=\frac{Q}{I}$, where $t$ is the time, $Q$ is the charge, and $I$ is the current. So $t=\frac{1420\ \text{mAh}}{900.0\ \text{mA}}\approx1.5778\ \text{h}$.

Step3: Convert hours to minutes and seconds

$1.5778\ \text{h}=1\ \text{h}+0.5778\ \text{h}$. Since $1\ \text{h} = 60\ \text{min}$, $0.5778\times60 = 34.668\ \text{min}=34\ \text{min}+0.668\ \text{min}$. And since $1\ \text{min}=60\ \text{s}$, $0.668\times60 = 40.08\ \text{s}\approx40\ \text{s}$. So $t = 1\ \text{h}\ 34\ \text{min}\ 40\ \text{s}$. But if we calculate more precisely:
$t=\frac{1420}{900}\text{h}=\frac{1420}{900}\times60\text{min}=\frac{1420\times60}{900}\text{min}=\frac{85200}{900}\text{min}=94.666\cdots\text{min}=94\text{min}+0.666\cdots\text{min}$. $0.666\cdots\times60 = 40\text{s}$. So $t = 94\ \text{min}\ 40\ \text{s}\approx94\ \text{min}\ 41\ \text{s}$

Answer:

94 minutes, 41 seconds