Question

The wire is broken on the right side of the circuit in FIGURE Q28.3. What is the potential difference $V_1-V_2$between points $1\mathrm{and}2$? Explain.

Short answer

The potential difference between the two points is given by$\mathbf{∆}{\mathit{V}}_{\mathbf{12}}\mathbf{=}\mathbf{3}\mathbf{}\mathit{V}$

Step-by-step solution

Given information and formula used 

Given :

The wire is broken on the right side of the circuit in the given figure :

Theory used :

Ohm's law, description of the relationship between current, voltage, and resistance. The amount of steady current through a large number of materials is directly proportional to the potential difference, or voltage, across the materials.

Determining the potential difference between points 1 and 2

The resistor creates a voltage drop for the battery when the wire is connected, and the current flowing through the resistance is determined by Ohm's equation as $I=\frac{3V}{3\Omega }=1A$

The current through the resistance is zero, that is$I=0$when the wire is broken, and there is no voltage drop for the battery.

Hence the two points $1\mathrm{and}2$have the same potential difference as the battery. So

$\mathbf{∆}{\mathit{V}}_{\mathbf{12}}\mathbf{=}\mathbf{3}\mathbf{}\mathit{V}$