Question

What is the total amount of energy stored in a 12-V, 85-A h car battery when it is fully charged?

Answer 1

Concepts and reason

This problem is based on the concept of power dissipated through an electrical component and energy stored in the electrical component.

The power dissipated is to be calculated and then this value of power is to be used to calculate the total amount of energy stored.

Fundamentals

Power: The power dissipated by an electrical circuit element is given by the product of that current and voltage.

Energy: Energy is defined as the ability to do some work.

Write the expression to calculate the power.

$P = VI$

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

Write the expression to calculate the energy.

$E = Pt$

Here, $E$ is energy and $t$ is time.

The current and voltage rating of a battery represents the current that can be drawn from the battery in one hour to discharge it completely. The $V{\rm{ - }}I$ rating gives the power.

Write the expression to calculate the power.

$P = VI$

Substitute $12{\rm{ V}}$ for $V$ and $85{\rm{ A}}$ for $I$.

$\begin{array}{c}\\P = \left( {12{\rm{ V}}} \right)\left( {85{\rm{ A}}} \right)\\\\ = 1020{\rm{ W}}\\\end{array}$

Calculate the energy stored in one hour.

Write the expression to calculate the energy.

$E = Pt$

Substitute $1020{\rm{ W}}$ for $P$ and $1{\rm{ hour}}$ for $t$.

$\begin{array}{c}\\E = \left( {1020{\rm{ W}}} \right)\left( {1{\rm{ hour}}\left( {\frac{{3600{\rm{ s}}}}{{1{\rm{ hour}}}}} \right)} \right)\\\\ = 3.67 \times {10^6}{\rm{ J}}\\\end{array}$

Ans:

The energy stored in the car battery is $3.67 \times {10^6}{\rm{ J}}$.