Question #41090

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Answer 1 · 2017-02-24T05:29:21

Time to charge the battery is 15.4 hours.

$2.0 M J$ $2.0 MJ$ is a unit of energy which is defined as power multiplied by time.

$E = P \times t$ $E = P xx t$

We know that: $1 M J$ $1MJ$ of energy = $277.8 W h$ $277.8Wh$

So $2.0 M J = 2.0 \times 277.8 = 555.6 W h$ $2.0 MJ = 2.0 xx 277.8 = 555.6Wh$

Note the is decimal is rounded off here to match the single decimal place in all the given values.

The battery charger uses $40.0 W$ $40.0W$ of power, but it only supplies $90 %$ $90%$ or $\frac{9}{10}$ $9/10$ of that power to the battery.

Then: $P = 40.0 \times \frac{9}{10} = 36.0 W$ $P = 40.0 xx 9/10 = 36.0 W$

Substituting these values into the equation;

$E = P \times t$ $E = P xx t$

$555.6 W h = 36.0 W t$ $555.6Wh = 36.0Wt$

$t = \frac{555.6}{36.0} = 15.4 h$ $t = 555.6/36.0 = 15.4h$