2.1 Charge, current, voltage, and power

Charge, current, voltage, and power are the building blocks of electrical systems. They describe how electricity moves and does work in circuits. Understanding these quantities and how they relate to each other is essential before you can analyze any real circuit.

These four quantities are tightly interconnected through relationships like Ohm's Law and the power equation. Once you're comfortable with them, you'll have the foundation for everything else in this course.

Charge and Current

Electric Charge and the Coulomb

Electric charge is a fundamental property of matter that causes it to experience a force in an electromagnetic field. Charges come in two types: positive and negative. Opposite charges attract, and like charges repel.

The unit of charge is the coulomb (C), named after Charles-Augustin de Coulomb.

• One coulomb equals the charge transferred by a current of one ampere flowing for one second: $1\text{ C} = 1\text{ A} \cdot 1\text{ s}$
• A single electron carries a charge of approximately $-1.602 \times 10^{-19}$ C, and a proton carries $+1.602 \times 10^{-19}$ C

That tiny per-particle charge means it takes roughly $6.24 \times 10^{18}$ electrons to make up one coulomb. You won't usually work at the individual electron level, but it helps to appreciate just how many charges are moving when even a small current flows.

Current and the Ampere

Current is the rate at which electric charge flows through a material. It's measured in amperes (A), where one ampere equals one coulomb of charge passing a point per second:

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

Here $I$ is current, $Q$ is charge in coulombs, and $t$ is time in seconds.

Current comes in two main forms:

• Direct current (DC) flows in one direction consistently, like in a battery-powered circuit.
• Alternating current (AC) periodically reverses direction, like the power delivered to household outlets.

One thing that trips people up: conventional current is defined as the direction positive charges would flow, from the positive terminal to the negative terminal. In reality, current in metal wires is carried by electrons moving the opposite way. Both conventions give the same results in circuit analysis, but most textbooks and this course use conventional current direction.

Voltage and Electric Fields

Voltage and the Volt

Voltage is the difference in electric potential energy per unit charge between two points. Think of it as the "pressure" that pushes charges through a circuit. A higher voltage means a stronger push.

The unit is the volt (V), named after Alessandro Volta:

$1\text{ V} = \frac{1\text{ W}}{1\text{ A}} = \frac{1\text{ J}}{1\text{ C}}$

That second form is worth remembering: one volt means each coulomb of charge gains (or loses) one joule of energy as it moves between those two points.

A note on terminology: voltage is sometimes called electromotive force (EMF) when referring specifically to the energy source (like a battery), and potential difference when referring to the voltage across a component. For most circuit analysis, you'll just call it voltage.

Electric Fields and Potential Difference

An electric field exists in the region around a charged object. Any other charge placed in that field experiences a force.

• Electric field strength is measured in volts per meter (V/m).
• For a uniform field, the relationship between voltage, field strength, and distance is: $V = Ed$, where $E$ is the electric field strength and $d$ is the distance between two points along the field direction.

Electric fields can be visualized with field lines. These lines point in the direction a positive test charge would move. They originate on positive charges and terminate on negative charges, and the closer the lines are packed together, the stronger the field.

At this intro level, you'll mostly use voltage directly in circuit problems rather than working with electric fields. But understanding that voltage comes from an underlying electric field helps the concept make more physical sense.

Power and Ohm's Law

Power and the Watt

Power is the rate at which energy is transferred or converted. The unit is the watt (W):

$1\text{ W} = \frac{1\text{ J}}{1\text{ s}}$

In electrical circuits, power equals voltage times current:

$P = VI$

For example, a 12 V battery supplying 5 A of current delivers $12 \times 5 = 60\text{ W}$ of power.

By substituting Ohm's Law into the power equation, you get two additional forms that are very useful:

• $P = I^2 R$ (useful when you know current and resistance)
• $P = \frac{V^2}{R}$ (useful when you know voltage and resistance)

All three forms give the same answer; which one you pick depends on what quantities you already know.

Ohm's Law

Ohm's Law states that the voltage across a conductor is directly proportional to the current through it, as long as temperature and other physical conditions stay constant:

$V = IR$

You can rearrange this to solve for any of the three quantities:

• $I = \frac{V}{R}$
• $R = \frac{V}{I}$

Resistance is measured in ohms ($\Omega$), named after Georg Ohm. One ohm is the resistance that produces one ampere of current when one volt is applied: $1\text{ }\Omega = \frac{1\text{ V}}{1\text{ A}}$.

Here's a quick example: a $10\text{ }\Omega$ resistor connected across a 5 V source draws $I = \frac{5}{10} = 0.5\text{ A}$. The power dissipated by that resistor is $P = VI = 5 \times 0.5 = 2.5\text{ W}$, or equivalently $P = I^2R = (0.5)^2 \times 10 = 2.5\text{ W}$.

One important caveat: Ohm's Law applies to ohmic (linear) materials, where resistance stays constant regardless of voltage. Components like diodes and transistors are non-ohmic, meaning their resistance changes with voltage or current. You'll encounter those later, but for now, most problems assume ohmic behavior.