Chapter 18, Problem 58GP

To determine

Time up to a fresh $12V$ battery last if it is rated at $95A\cdot h$ .

Answer to Problem 58GP

  $12.38hours$

Explanation of Solution

Given info:

Current, $I=95A.h$

Power, $P=92W$

Voltage, $V=12V$

Formula used:

Relationship between charge $Q$ , current $I$ , and time $t$ : $Q=It$

By the definition of the power, $P=VI$

Where, $P$ is power, $V$ is voltage and $I$ is current.

Calculation:

First calculate the $Q$ by using the formula, $Q=It$

  $Q=95A\cdot h\times 3600s=342000C$

Now, convert $A\cdot h$ to $A\cdot s$ to work in SI units.

Rearrange the expression, $P=VI$ . So, $I=\frac{P}{V}$

Substitute the given values in the expression: $I=\frac{P}{V}$

  $I=\frac{92}{12}=7.67A$

Again, use the formula $Q=It$ , to calculate the time.

  $t=\frac{Q}{I}=\frac{342000}{7.67}=44,589.308s=12.38hours$

Conclusion: Time up to a fresh $12V$ battery last if it is rated at $95A\cdot h$ is $12.38h$ .