Chapter 19, Problem 24P

To determine

The terminal voltage of the each battery.

Answer to Problem 24P

The terminal voltage of the first battery is $17.375\text{V}$ and the terminal voltage of the second battery is $13.25\text{V}$ .

Explanation of Solution

Given info:

The internal resistance of the first battery is, $r_1=1\Omega$ .

The voltage of the first battery is, ${\epsilon }_1=18\text{V}$ .

The internal resistance of the second battery is, $r_2=2\Omega$ .

The voltage of the second battery is, ${\epsilon }_2=12\text{V}$ .

The resistance in the circuit is, $R=6.6\Omega$ .

Formula Used:

The expression to calculate the current in the circuit is,

  $I=\frac{{\epsilon }_2-{\epsilon }_1}{r_1+r_2+R}$

The expression to calculate the terminal voltage of the first battery is,

  $V_1={\epsilon }_1-I{r}_1$

The expression to calculate the terminal voltage of the second battery is,

  $V_2={\epsilon }_2+I{r}_2$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}I=\frac{18\text{V}-12\text{V}}{1\Omega +6.6\Omega +2\Omega }\\ =0.625\text{A}\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}{V}_1=18\text{V}-\left(0.625\text{A}\right)\left(1\Omega \right)\\ =17.375\text{V}\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}{V}_2=12\text{V}+\left(0.625\text{A}\right)\left(2\Omega \right)\\ =13.25\text{V}\end{array}$

Conclusion:

Therefore, the terminal voltage of the first battery is $17.375\text{V}$ and the terminal voltage of the second battery is $13.25\text{V}$ .