Voltage is a difference, not a label

Two points define a voltage

A voltage is the electric potential difference between two points. Writing “node A is 3 V” means 3 V relative to a stated reference, usually the node named ground. Ground is a bookkeeping reference; it does not automatically mean an earth connection. A battery can power a circuit whose entire reference floats relative to your room.

Define $V_{AB}=V_A-V_B$. If A is 3.3 V and B is 1.2 V, the voltage from A to B is 2.1 V. Reversing the meter leads gives −2.1 V. Negative values therefore convey direction, rather than an impossible electrical state. Name nodes before calculating and carry the polarity through each equation.

A first resistor calculation

For an ideal resistor, Ohm's law is $V=IR$. A 2.2 kΩ resistor carrying 1.5 mA has 3.3 V across it: $2200\times0.0015=3.3$. The kilo and milli factors cancel here, but only because their exponents are opposite. With 220 Ω instead, the same current produces 0.33 V. Always write a line in base units when a result seems surprising.

A (3.3 V) --- R = 2.2 kohm --- B (0 V)
                  I = 1.5 mA -->

This drawing declares positive current from A to B and positive resistor voltage at A. It describes a two-terminal relationship, not a guarantee that a real source can deliver the requested current. A supply current limit, resistor tolerance, and wire resistance may change the result.

Read before connecting

Place a voltage meter across the two nodes while leaving the circuit connected. Its finite input resistance becomes another circuit branch; we will calculate that loading later. For the course, use low-voltage examples with a 3.3 V or 5 V source. Record source value, reference, resistor value, and expected voltage before a measurement. This habit separates a wiring error from an arithmetic error.