Voltage, Current, and Ground

The puzzle

A microcontroller pin says “3.3 V”. Three point three volts relative to what? A battery is rated in volts, a resistor in ohms, an LED wants milliamps, and “ground” appears on every schematic, sometimes as three little lines, sometimes as a word. Before anything digital makes sense, these four ideas need to be solid: voltage, current, resistance, and the reference point everything is measured from.

STEP 1

Voltage is always between two points

Voltage is a difference in electrical potential energy per unit of charge. The unit is the volt (V), and the word to hold onto is difference. A single point does not have a voltage on its own, any more than a single point on a hill has a height on its own. Height only means something once you say “above sea level” or “above the floor”. Voltage only means something once you say which second point you are comparing with.

So “the pin is at 3.3 V” is shorthand for “the pin is 3.3 V above the point we agreed to call zero”. That agreed point is ground, and we will come back to it. Voltage across a component (the difference between its two ends) is what pushes current through it.

STEP 2

Current is a flow through a branch

Current is the rate at which charge passes a point, measured in amperes (A): one ampere is one coulomb of charge per second. Where voltage is measured across something, current is measured through something. A wire, a resistor, an LED, a pin: current flows through each of them, and in a simple loop the same current flows through every part in turn. Nothing accumulates in the resistor; what goes in one end comes out the other.

Embedded circuits mostly live in milliamps (mA, thousandths) and microamps (µA, millionths). A small LED might take 5 mA; a sleeping microcontroller might draw a few µA.

STEP 3

The loop

↑ This step uses the figure at the top of the page.

Current needs a closed path. The source raises the potential of charge at its + terminal, the charge flows out through the wire, drops its energy in the resistor, and returns to the − terminal of the source to be lifted again. Break the loop anywhere, an open switch, a cut wire, a missing return connection, and the current stops everywhere in the loop, not just at the break. This is the single most useful debugging fact in electronics: no return path, no current, no matter how confident the supply looks.

Slide the voltage and resistance above. The current follows one relationship, Ohm’s law:

I = \frac{V}{R}

where $I$ is the current in amperes, $V$ is the voltage across the resistor in volts, and $R$ is its resistance in ohms (Ω). The graph on the right is the whole story for a resistor: a straight line through the origin whose slope is $1/R$ . Double the voltage, double the current; double the resistance, halve the current.

STEP 4

Which way does it flow?

Schematics use conventional current: it flows from higher potential to lower, out of the + terminal, through the load, into the −. A forward-biased diode conducts from anode to cathode; the small outward arrows on an LED symbol represent emitted light, not current. Physically, electrons in a metal are negatively charged and drift opposite to conventional current. Conventional current is defined by positive-charge flow; neither description is incorrect. Toggle electron motion in the diagram to see both.

Two things the moving markers must not make you believe:

They do not show electron speed. In a copper wire carrying a few amps, electrons drift at millimetres per second or less; HyperPhysics works a 3 A, 1 mm wire example to 0.28 mm/s. The current starts everywhere in the loop almost instantly because the electric field is established at a large fraction of the speed of light, and all the electrons already in the wire begin to move together.
They do not show a signal “travelling” from the chip to the LED and “replying”. There is one loop and one current in it.

STEP 5

Ground is a choice, not a drain

INTERACTIVEGround is a choice of reference

Node used as ground (0 V)

Ground at C: V_A = +9 V, V_B = +6 V, V_C = 0 V. Differences stay put: V_A − V_B = 3 V, V_B − V_C = 6 V, I = 3 mA.

Two resistors in series across a 9 V source. Pick which node is called 0 V. Every node voltage changes, but the voltage across each resistor does not, and the current does not. Ground is the point you measure from, not a place where current vanishes: the current that flows into it flows back to the source.

Because voltage is a difference, you are free to pick any node as the reference and call it 0 V. That node is ground. Move the reference in the figure: every node label changes, but the voltage across each resistor and the current through the loop stay exactly the same. The circuit does not know which node you called zero.

Two consequences matter for embedded work:

Ground is not a sink. Current that flows “into ground” flows back to the supply through the ground wire or plane. If that return wire is thin, long or missing, the circuit misbehaves even though every ground symbol on the schematic looks identical.
Two boards share ground only if you connect them. A sensor on one board and a microcontroller on another can each have a perfectly good 3.3 V, yet the signal wire between them means nothing until their grounds are joined. The receiver measures the signal against its ground.

Chassis ground, earth ground and signal ground are different things that may or may not be connected; the symbol tells you which node is the reference, not where the current goes.

STEP 6

Power: where the energy ends up

Charge loses energy as it passes through the resistor, and that energy becomes heat. The rate is power, in watts:

P = V \cdot I

with $V$ the voltage across the part and $I$ the current through it. Substituting Ohm’s law gives two more forms that are often handier:

P = I^2 R

P = \frac{V^2}{R}

A 1/4 W resistor really will get uncomfortably hot at 1/4 W, so leave margin: keeping a part below half of its rating is a common rule of thumb, not a law, and the resistor’s datasheet derating curve is the real limit.

STEP 7

Worked example: sizing a resistor

A 5 V supply must push about 10 mA through a resistor. What resistance, and how much power will it dissipate?

R = \frac{V}{I} = \frac{5\ \text{V}}{0.010\ \text{A}} = 500\ \Omega

Standard values near 500 Ω are 470 Ω and 510 Ω. With 470 Ω:

I = \frac{5}{470} = 10.6\ \text{mA}

P = V \cdot I = 5 \times 0.0106 = 53\ \text{mW}

A 1/4 W (250 mW) resistor is comfortably rated. Set the figure at the top to 5 V and 470 Ω and read the same numbers off the annotation.

STEP 8

Measuring: where the meters go

DIAGRAMWhere a voltmeter and an ammeter go

Voltmeter: in parallel, high resistance. Ammeter: in series, very low resistance.

A voltmeter measures the difference between two points, so it connects across the part (in parallel) and draws almost no current. An ammeter measures what flows through a branch, so the wire is opened and the meter is inserted in series. Swapping them is the classic mistake: a voltmeter in series stops the circuit, and an ammeter across a source is a short circuit.

A voltmeter reports the difference between its two probes, so it goes across the part, in parallel with it. It has a very high internal resistance (megohms), so it steals almost no current and barely disturbs the circuit.

An ammeter reports what flows through it, so the loop must be opened and the meter inserted in series. It has a very low internal resistance so that it drops almost no voltage.

Swap them and things go wrong in opposite ways. A voltmeter in series adds megohms to the loop, so the current collapses to nearly nothing and the circuit stops working while you measure it. An ammeter across a source is a near-short: the source pushes as much current as it can through the meter, which pops the meter’s fuse if you are lucky.

MYTHS AND FACTS

Common misconceptions

Ground is where current goes to disappear

It returns to the supply. Every loop closes.

A voltage exists at a point

Only relative to a reference. Two 3.3 V nodes on two unconnected boards are not at the same potential in any useful sense.

The supply pushes a fixed current

An ordinary voltage source holds its voltage; the load decides the current through $I = V/R$ . A 5 V, 2 A supply delivers 2 A only if the load asks for it.

Current is used up in the resistor

Energy is used up; the current entering equals the current leaving.

Electrons race around the loop

They drift slowly. The field, not the electron, is what arrives quickly.

Check yourself

Answer in your head, then open the card.

A 9 V battery drives a 4.7 kΩ resistor. What current flows, and roughly what power does the resistor dissipate?

$I = 9 / 4700 = 1.9$ mA. $P = V \cdot I = 9 \times 0.0019 \approx 17$ mW, far below a 1/4 W rating.

In the ground-reference figure, set ground to node B. Node C reads −6 V. Has the current through R2 changed?

No. The current is still 3 mA, because the voltage across R2 (V_B − V_C = 0 − (−6) = 6 V) is unchanged. Only the labels moved.

You connect a sensor’s output wire to a microcontroller input but forget the ground wire between the two boards. Why does the reading make no sense?

The microcontroller measures the input relative to its own ground. Without the ground wire there is no shared reference and no return path for any current, so the “signal” it sees is undefined.

Why does a voltmeter in series with a resistor seem to “kill” the circuit?

The meter’s internal resistance is millions of ohms. In series it dominates the loop, so the current drops to microamps and the resistor sees almost no voltage. The meter is not broken; it is in the wrong place.

Sources (3)

Tony R. Kuphaldt, Lessons in Electric Circuits, Vol. I (DC), ch. 1 “Basic Concepts of Electricity” — conventional versus electron flow; the direction convention used on schematics
Tony R. Kuphaldt, Lessons in Electric Circuits, Vol. I (DC), ch. 2 “Ohm’s Law” — E = IR and P = IE, with the historical attribution to Ohm and Joule
R. Nave, HyperPhysics (Georgia State University), “Microscopic View of Ohm’s Law” — electron drift velocity of the order of millimetres per second, versus near-light-speed signal propagation