Chapter 19, Problem 26P

To determine

The potential difference between the points a and point b .

Answer to Problem 26P

The potential difference between the point a and point b is $0\text{V}$ .

Explanation of Solution

Given info:

The voltage of each battery is, $V_{1/2}=1.5\text{V}$ .

The resistance of each resistor is, $R_{1/2/3/4}=75\Omega$

Formula Used:

The expression to calculate the current in the circuit is,

  $I=\frac{V_1+V_2}{R_1+R_2+R_3+R_4}$

The expression to calculate the potential difference between the point a and point b is,

  $V_{ab}=V-I\left(R_1+R_2\right)$

Calculation:

Substitute all the values in the above expression.

  $\begin{array}{c}I=\frac{1.5\text{V}+1.5\text{V}}{75\Omega +75\Omega +75\Omega +75\Omega }\\ =0.01\text{A}\end{array}$

Substitute all the values in the above expression.

  $\begin{array}{c}{V}_{ab}=1.5\text{V}-\left(0.01\text{A}\right)\left(75\Omega +75\Omega \right)\\ =0\text{V}\end{array}$

Conclusion:

Therefore, the potential difference between the point a and point b is $0\text{V}$ .