Voltage, Current, and Resistance

Definition: Voltage is the electrical potential difference that pushes charge through a circuit, current is the rate of flow of that charge, and resistance is the opposition a material offers to that flow.

How It Works

Voltage (V, volts) is measured across two points, a difference in electrical potential energy per unit charge, sometimes called electromotive force at a source
Current (I, amps) is measured through a path, the rate at which charge (in coulombs) flows past a point per second
Resistance (R, ohms) is a property of the conductor or component that opposes current flow, converting some electrical energy into heat
The classic water analogy: voltage is like water pressure, current is like flow rate (gallons per minute), and resistance is like a narrow pipe restricting that flow
The three are linked directly through Ohm’s Law: raise resistance and current drops for the same applied voltage; raise voltage and current rises for the same resistance
Conventional current is defined as flowing from positive to negative terminal, even though the actual electrons physically move in the opposite direction
Conductance, the reciprocal of resistance, describes how easily a material passes current, measured in siemens (S)
Materials range from conductors (very low resistance, like copper) to insulators (very high resistance, like rubber) to semiconductors (resistance controllable in between, like silicon)
Superconductors, cooled to extremely low temperatures, exhibit exactly zero resistance, letting current flow indefinitely without any energy loss to heat
Internal resistance inside a real battery or power source means its terminal voltage sags slightly under load, a detail the simplest circuit models often ignore
Static electricity buildup, like a shock from touching a doorknob, involves very high voltage (thousands of volts) but negligible charge and current, which is why it startles rather than harms
Human body resistance varies widely with skin moisture and contact area, which is why the same voltage can be barely noticeable in dry conditions but dangerous with wet skin
Series and parallel resistor networks reduce to a single equivalent resistance, letting complex-looking circuits be simplified step by step down to one V, I, and R relationship

Units at a Glance

Volt (V) — one joule of energy per coulomb of charge moved between two points
Ampere (A) — one coulomb of charge passing a point per second
Ohm (Ω) — the resistance that allows one ampere of current to flow when one volt is applied
Coulomb (C) — the base unit of electric charge, roughly 6.24 × 10¹⁸ electrons
Siemens (S) — the unit of conductance, the reciprocal of the ohm

Illustration

Under the Hood

Ohm’s Law, the core relationship linking all three:

V = I × R

Current defined as charge flow rate:

I = Q / t

where Q is charge in coulombs, t is time in seconds.

Resistance from material properties:

R = ρ × (L / A)

where ρ is resistivity, L is conductor length, A is cross-sectional area.

Worked Problem 1: finding current from voltage and resistance Given: a 9V battery is connected across a 100 Ω resistor to light an LED (ignoring LED forward voltage for simplicity). Step 1: Apply Ohm’s Law: I = V / R. Step 2: I = 9 V / 100 Ω. Answer: I = 0.09 A, or 90 mA.

Worked Problem 2: charge flow over time Given: a circuit carries a steady current of 2 A for 30 seconds. Step 1: Q = I × t. Step 2: Q = 2 A × 30 s. Answer: Q = 60 coulombs of charge passed through the circuit.

Worked Problem 3: resistance of a copper wire Given: a copper wire is 5 meters long with a cross-sectional area of 2×10⁻⁶ m² (about 2 mm²), copper resistivity ρ ≈ 1.68×10⁻⁸ Ω·m. Step 1: R = ρ × (L / A). Step 2: R = 1.68×10⁻⁸ × (5 / 2×10⁻⁶). Step 3: R = 1.68×10⁻⁸ × 2,500,000. Answer: R ≈ 0.042 Ω, illustrating why copper wiring over short distances has negligible resistance compared to most circuit components.

Worked Problem 4: two resistors in series Given: a 12V battery drives a circuit with a 47 Ω resistor in series with a 33 Ω resistor. Step 1: Total resistance = 47 Ω + 33 Ω = 80 Ω. Step 2: I = V / R = 12 V / 80 Ω. Step 3: I = 0.15 A. Step 4: Voltage across the 47 Ω resistor = I × R = 0.15 A × 47 Ω = 7.05 V. Answer: 0.15 A flows through both resistors, with 7.05 V dropped across the 47 Ω resistor and the remaining 4.95 V across the 33 Ω resistor.

Why It Matters

Nearly every circuit calculation and component rating starts from these three quantities: fuse sizing, wire gauge selection, and power dissipation calculations all build on them
Safety ratings for equipment, insulation, and human contact limits are all derived from how much current a given voltage can drive through a given resistance path, including the human body
Understanding the relationship lets engineers predict circuit behavior before building anything, rather than relying on trial and error
Misjudging any one of the three, applying too much voltage, drawing too much current, or underestimating resistance-driven heating, is the root cause of most component failures
Multimeters measure all three quantities directly, making them the single most useful diagnostic tool for troubleshooting any circuit

Common Pitfalls

Confusing voltage (a difference between two points) with a single-point quantity; voltage always needs a reference point to be meaningful
Assuming current is “used up” as it flows through a circuit, when in a series circuit the same current flows through every component, only voltage is divided
Forgetting resistance is temperature-dependent for most conductors, so a component’s resistance at operating temperature can differ noticeably from its rated value at room temperature
Treating a wire’s resistance as always negligible; for long runs or high currents, wire resistance causes real voltage drop and heating
Mixing up conventional current direction (positive to negative) with actual electron flow (negative to positive) when reasoning about diode or transistor behavior
Applying Ohm’s Law to non-ohmic components like diodes or LEDs, which don’t have a fixed linear resistance and require different analysis
Measuring current with a multimeter set to voltage mode (or vice versa), which either reads nothing useful or, worse, creates a short circuit through the meter
Forgetting that a voltmeter should be placed in parallel and an ammeter in series, wiring them backward and getting no reading or blowing the meter’s internal fuse

Comparison

Quantity	Symbol	Unit	Measured	Water Analogy
Voltage	V	Volt (V)	Across two points	Water pressure
Current	I	Ampere (A)	Through a path	Flow rate
Resistance	R	Ohm (Ω)	Property of a component	Pipe narrowness
Power (derived)	P	Watt (W)	Product of V and I	Rate of energy delivered
Conductance (derived)	G	Siemens (S)	Reciprocal of resistance	Pipe wideness

Comparison: Conductors vs Semiconductors vs Insulators

	Conductor	Semiconductor	Insulator
Typical resistivity	Very low (~10⁻⁸ Ω·m)	Moderate, adjustable	Very high (~10¹⁶ Ω·m)
Example	Copper, silver, aluminum	Silicon, germanium	Rubber, glass, plastic
Behavior	Current flows freely	Current controllable via doping/voltage	Current essentially blocked

History

Alessandro Volta invented the first practical chemical battery, the voltaic pile, in 1800, and the volt is named in his honor
André-Marie Ampère’s early 19th-century work on electrodynamics established the mathematical relationship between electric current and magnetism, giving the ampere its name
Georg Ohm published his law relating voltage, current, and resistance in 1827, though it was initially met with skepticism before becoming one of the most fundamental relationships in electrical engineering
The ohm, volt, and ampere were formally standardized as units at international electrical congresses in the late 19th century, enabling consistent measurement across countries and manufacturers
Benjamin Franklin’s mid-18th century convention of calling one type of charge “positive” and the other “negative” predates the discovery of the electron, which is why conventional current direction and actual electron flow end up opposite

Example

A 9V battery pushing current through a 100Ω resistor to light an LED draws about 90 mA of current (ignoring the LED’s own forward voltage drop), following directly from I = V/R.

A car battery’s jumper cables illustrate all three quantities at once: the battery provides voltage (typically 12V), the starter motor’s resistance sets how much current flows, and thick cables minimize added resistance so as little voltage as possible is wasted before it reaches the starter.

FAQ

Why do birds sitting on a high-voltage power line not get electrocuted? Because both of the bird’s feet are at nearly the same voltage (touching the same wire), there’s essentially no voltage difference across the bird’s body, so almost no current flows through it.

Is resistance always constant for a given component? No, resistance in many real materials changes with temperature, and non-ohmic components like diodes and transistors don’t follow a simple linear V = IR relationship at all.

What’s the difference between EMF and voltage? EMF (electromotive force) refers specifically to the energy per charge a source (like a battery) provides; voltage is the more general term for potential difference between any two points, including drops across resistive loads.

Why is current the same throughout a series circuit but voltage divides? Charge has nowhere else to go in a series path, so the same current must flow through every component in sequence, while each component consumes (drops) a portion of the total voltage based on its resistance.

Why does resistance generate heat? As charge carriers move through a resistive material, they collide with the material’s atomic lattice, transferring kinetic energy as heat, an effect called Joule heating.

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