The phrase "the potential difference, VA−VBV_A-V_BVA−VB," in a circuit means the voltage difference between points A and B, calculated as the electric potential at point A minus the electric potential at point B. This is a standard convention where
VAB=VA−VBV_{AB}=V_A-V_BVAB=VA−VB
This quantity represents how much higher (or lower) the electric potential is at point A compared to point B. If VA−VBV_A-V_BVA−VB is positive, point A is at a higher electric potential than point B; if negative, then B has a higher potential than A. The potential difference between two points drives current flow in a circuit according to Ohm's Law and Kirchhoff's Laws. In the context of a circuit with resistances or voltage sources, the potential difference VA−VBV_A-V_BVA−VB can be found by summing the voltage rises and drops along a path from A to B. For instance, if the circuit has a 10kΩ resistor between points A and B, the potential difference across that resistor is related to the current through it by Ohm’s Law:
VA−VB=I×10kΩV_A-V_B=I\times 10k\Omega VA−VB=I×10kΩ
where III is the current flow from A to B direction. Therefore, if it is given that the potential difference VA−VBV_A-V_BVA−VB equals k×10kk\times 10kk×10k, presumably meaning kkk times 10 kilo-ohms, it would commonly relate to a voltage drop or rise defined in terms of that resistor's resistance and current or a product involving those values in the circuit. To give a precise interpretation or calculation, details of what kkk is or the current in the circuit are needed. Fundamentally,
- VA−VBV_A-V_BVA−VB is the voltage difference (potential difference) from point A to point B.
- Across a resistor, it equals current times resistance (Ohm's Law).
- A positive value means point A is at higher potential.
This standard usage applies in conventional circuit analysis of VA−VBV_A- V_BVA−VB for potential difference across components or nodes.
