Question

The open circuit voltage of a standard car battery is 12.6 V, and the short circuit current is approximately 300 A. What is the available power from the battery?

Answer 1

Answer:

11.25V is the available power from the battery

Answer 2

Step by step Explanation:

Given:

Voltage of car battery $V_{oc} =12.6V$

Current in short circuit $I_{sc} =300A$

To find:

Available power from the battery( $P_{avl}$ )

Solution:

We determine the output impedance of the battery,

                         $R_0=\frac{V_{oc}}{I_{sc}}$

                              $=\frac{12.6}{300}$

                        $R_0=0.042 \;\Omega$

Therefore the available is ,

                       $P_{avl}=I^2RL$

                               $=\left[\frac{V_{Th}}{R_{Th}+R_L}\right]^2\times R_L$

                               $=\left[\frac{V_{Th}}{R_{Th}+R_L}\right]^2\times R_{Th}$

                       $P_{avl}=\frac{{V^2}_{Th}}{4R_{Th}}$

Substitute the $V_{oc$ , $I_{sc$ values in $P_{avl$ equation,

$P_{avl}=\frac{{V^2}_{Th}}{4R_{Th}}=\frac{V_{oc}^{\;2}}{4R_0}$

      $=\frac{{(12.6)}^2}{4\times0.042}$

      $=$  $945W$

$P_{avl$ $=$ $945W$

Finally the Available Power of the battery $945W$