B) 37 V
The potential difference between point a and point b is equal to 37 V
Explanation:
The potential difference across a and b can be calculated by finding the equivalent resistance of the resistors R1, R2 and R3 and then by applying Ohm's law.
Given:
R1 = 3.0 Ω
R2 = 8.0 Ω
R3 = 10.0
Current = I = 5 A
To calculate equivalent resistance of the circuit:
R2 and R3 are connected in parallel configuration. The equivalent resistance of R2 and R3 can be calculated as
[tex]\frac{1}{R_p} =\frac{1}{R_2} + \frac{1}{R_3} \\\\\frac{1}{R_p}=\frac{1}{8} + \frac{1}{10}= \frac{5+4}{40} = \frac{9}{40} \\\\ \frac{1}{R_p}=\frac{9}{40} \\\\R_p=\frac{40}{9}\ ohms[/tex]
Resistance R1 is in series with Rp. The equivalent series resistance is calculated as
[tex]R_s = R1+R_p = 3+\frac{40}{9}= \frac{27+40}{9} = \frac{67}{9} = 7.44\ ohms[/tex]
Thus the given 3 resistor circuit can be written as an equivalent resistance Rs equal to 7.44 Ω through which current I passes.
By Ohm's law;
If V is the potential difference between a and b
Potential difference across points a and b = Current flowing through the circuit × Resistance between points a and b
[tex]V = I\times R_s = 5\times 7.44 = 37.2\ V[/tex]
37.2 V ≈ 37 V
Therefore, the potential difference between point a and point b is equal to 37 V
