Fundamental Electrical Quantities and Symbols

Circuit equations are compact descriptions of measurable physical quantities. Reading them correctly requires three things: the quantity symbol, its unit, and the two points or direction used as a reference.

Learning objectives

After this lesson, you will be able to:

• define charge, current, voltage, resistance, conductance, power, and energy;
• distinguish a quantity symbol from a unit symbol;
• use SI prefixes without losing factors of one thousand;
• identify common schematic symbols and reference designators;
• apply passive sign convention to decide whether an element absorbs or supplies power.

Core quantities

• Charge, Q or q: measured in coulombs (C); the amount of electric charge.
• Current, I or i: measured in amperes (A); I = dQ/dt.
• Voltage, V or v: measured in volts (V); energy per charge, V = W/Q.
• Resistance, R: measured in ohms (Ω); R = V/I for an ohmic element.
• Conductance, G: measured in siemens (S); G = 1/R.
• Power, P or p: measured in watts (W); P = VI.
• Energy, E or W: measured in joules (J); the integral of power over time.

The same letter can mean a quantity or appear in a unit, so typography and context matter. In V = 5 V, the first V names voltage and the second V means volts.

Charge and current

The elementary charge magnitude is approximately:

$$
e = 1.602,176,634 \times 10^{-19}\ \text{C}
$$

This value is exact in the SI definition. One coulomb corresponds to about 6.242 × 10¹⁸ elementary charges.

Current measures rate, not speed:

$$
I = \frac{\Delta Q}{\Delta t}
$$

If 3 C crosses a boundary in 2 s, the average current is 1.5 A.

Voltage is always between two points

Voltage is electric potential difference. Writing V_AB means the potential at node A relative to node B:

$$
V_{AB} = V_A - V_B
$$

If V_AB = -2 V, node A is two volts below node B. A negative answer is valid information, not a failed calculation.

Resistance and conductance

Resistance describes opposition to current in an ohmic element. Conductance describes ease of conduction:

$$
G = \frac{1}{R}
$$

A 2 kΩ resistor has a conductance of 0.5 mS.

Power and energy

Instantaneous electrical power is:

$$
p(t) = v(t)i(t)
$$

Using passive sign convention, current entering the terminal marked positive gives positive power for an absorbing element. Negative power means the element is delivering energy under the chosen references.

For constant DC values, a 5 V load drawing 200 mA absorbs:

$$
P = 5\ \text{V} \times 0.2\ \text{A} = 1\ \text{W}
$$

If it operates for 30 s, it receives 30 J of energy.

How the quantities relate

SI prefixes used in electronics

Prefix symbols are case-sensitive.

MΩ means megaohms; mΩ means milliohms—a difference of one billion.

Schematic notation

A schematic describes electrical connectivity and function, not physical placement. Common reference designators include:

Standards and organizations may use different graphical conventions, such as rectangular or zigzag resistor symbols. Connectivity, labels, and a drawing's declared convention matter more than visual familiarity.

Worked example: keep units visible

A sensor board draws 35 mA from 3.3 V for 10 s.

$$
P = 3.3\ \text{V} \times 0.035\ \text{A} = 0.1155\ \text{W}
$$

$$
E = Pt = 0.1155\ \text{W} \times 10\ \text{s} = 1.155\ \text{J}
$$

The board receives about 116 mW, and over ten seconds it receives about 1.16 J.

Interactive charge calculator

Enter any two values and leave the third blank.

Common mistakes

• Using V for voltage without naming its reference node.
• Calling current “the speed of electrons.”
• Confusing charge in coulombs with energy in joules.
• Writing M when m is intended.
• Assuming every component obeys a constant R = V/I.
• Reading a schematic as though it were a physical wiring layout.

Summary

• Every circuit quantity has a definition, symbol, unit, and reference.
• Voltage is energy per charge between two points.
• Current is charge transferred per unit time.
• Power is the rate of energy transfer; energy accumulates over time.
• Prefixes and polarity references are part of the engineering answer.

Next: Voltage Sources and Resistors in Series and Parallel.

Further reading

• NIST: SI Units
• NIST: Guide for the Use of the International System of Units
• IEC 60617 graphical symbols overview