3. Basic Electrical Principles

Learning Objectives

By the end of this page, you should be able to:

• Define electric charge, electric field, and electric potential, and explain how they relate to one another
• State Ohm's Law and use it to calculate voltage, current, or resistance given the other two quantities
• Explain the difference between a vector quantity (electric field) and a scalar quantity (electric potential)
• Calculate power dissipated in a resistive circuit using P = VI and its derived forms
• Describe how capacitance and inductance store energy differently from a resistor dissipating it
• Apply these principles to a simple real-world circuit, such as household wiring or an LED with a series resistor

Quick Answer

Every electronic circuit ultimately rests on a small set of physical quantities: charge (the fundamental property that creates electrical effects), electric field (the force per unit charge in a region around a charge), electric potential or voltage (the energy per unit charge, which drives current between two points), current (the actual flow of charge), and resistance (opposition to that flow). Ohm's Law, V = IR, ties voltage, current, and resistance together and is the single most-used equation in electronics. Power, P = VI, tells you how fast energy is converted to heat or work. Understanding these five ideas is non-negotiable — every resistor, capacitor, inductor, and semiconductor device you'll study later is just a more elaborate way of manipulating charge, field, and potential.

Electric Charge: Where It All Starts

Electric charge is a fundamental property of matter, carried by electrons (negative) and protons (positive). Charge is measured in coulombs (C), and one electron carries about 1.6 × 10⁻¹⁹ C — an extremely small amount, which is why practical currents involve enormous numbers of electrons moving together.

Two rules govern how charges behave: like charges repel, unlike charges attract, and the law of conservation of charge states that charge cannot be created or destroyed, only moved from one object to another (or separated, as when you rub a balloon on your hair). This conservation principle is why circuit analysis works at all — current flowing into a junction must equal current flowing out, because charge cannot simply vanish partway through a wire.

Electric Field: The Force Around a Charge

Any charged particle creates an electric field — a region of space in which another charge would feel a force. The field is a vector (it has both magnitude and direction) and is defined as the force a small positive "test charge" would experience at a point, divided by the size of that test charge: E = F/q.

Field strength falls off with the square of distance from the source charge (an inverse-square law, the same mathematical shape as gravity). This is why a charged object exerts a strong pull very close up but a negligible one a meter away. Field lines are the standard way to visualize this — they point in the direction a positive test charge would move, and they get denser where the field is stronger.

Electric Potential (Voltage): The Energy That Drives Current

Electric potential, commonly called voltage, is the potential energy per unit charge at a point: V = U/q, measured in volts. Unlike the electric field, potential is a scalar — it has a magnitude but no direction. What actually drives current through a circuit is not the potential at a single point, but the potential difference between two points, which represents the work done moving a unit charge from one point to the other.

This is why a 1.5 V battery is meaningful — it's not describing some absolute property of the battery, but the energy difference it can provide per coulomb of charge pushed from its negative terminal to its positive terminal through an external circuit.

Resistance and Ohm's Law: Connecting Voltage and Current

Resistance describes how strongly a material opposes the flow of current, measured in ohms (Ω). It depends on the material (copper resists less than nichrome), the geometry (thin, long wires resist more than thick, short ones), and temperature (resistance in most conductors rises as they heat up).

Ohm's Law ties voltage, current, and resistance together:

V = IR

where V is voltage in volts, I is current in amperes, and R is resistance in ohms. This equation lets you find any one quantity given the other two — a 12 V supply across a 4 Ω resistor drives 3 A of current (I = V/R = 12/4 = 3 A). Ohm's Law only holds exactly for "ohmic" materials like most resistors and metals at constant temperature — components like diodes and transistors do not follow a simple linear V-I relationship, which is exactly what makes them useful for switching and amplification rather than plain current limiting.

Power: The Rate of Energy Transfer

Power is the rate at which electrical energy is converted — into heat in a resistor, into light in an LED, into motion in a motor. It's calculated as:

P = VI

Combining this with Ohm's Law gives two other useful forms: P = I²R (useful when you know current and resistance) and P = V²/R (useful when you know voltage and resistance). A 100 W light bulb on a 230 V supply draws about 0.43 A (I = P/V), and a 10 Ω resistor carrying 2 A dissipates 40 W (P = I²R) — enough to require a resistor rated well above that to avoid burning out.

Capacitance and Inductance: Storing Rather Than Dissipating

Not every component just resists current — some store energy instead.

Capacitance (C, measured in farads) describes a component's ability to store charge in an electric field between two conductive plates separated by an insulator (the dielectric): C = Q/V. Capacitors are used to filter noise, smooth power supply ripple, and couple AC signals between amplifier stages while blocking DC.

Inductance (L, measured in henries) describes a coil's opposition to a change in current, caused by the magnetic field it generates: L = NΦ/I, where N is the number of turns and Φ is magnetic flux. Inductors resist sudden changes in current (producing a back-EMF), which makes them useful in filters, transformers, and switching power supplies, but also means they can produce dangerous voltage spikes if current through them is interrupted suddenly — which is why relay circuits include flyback diodes.

The key conceptual difference from a resistor: a resistor continuously dissipates energy as heat as long as current flows, while a capacitor or inductor stores energy and can return it to the circuit later.

Key Terms

Term	Definition	Related Concept
Electric charge	Fundamental property of matter causing electrical effects, measured in coulombs	Electron, proton, conservation of charge
Electric field	Region around a charge where a force would be felt by another charge; a vector quantity	Field lines, inverse-square law
Electric potential (voltage)	Potential energy per unit charge at a point; a scalar quantity, measured in volts	Potential difference, EMF
Current	Rate of flow of electric charge, measured in amperes	Conductor, circuit
Resistance	Opposition to current flow, measured in ohms	Ohm's Law, resistivity
Ohm's Law	V = IR, relating voltage, current, and resistance	Ohmic material, linear circuit
Power	Rate of energy transfer or conversion, measured in watts	P = VI, P = I²R, P = V²/R
Capacitance	Ability to store charge in an electric field, measured in farads	Dielectric, C = Q/V
Inductance	Opposition to a change in current, caused by a magnetic field, measured in henries	Back-EMF, L = NΦ/I
Conservation of charge	Principle that charge cannot be created or destroyed, only transferred	Kirchhoff's Current Law

Common Mistakes

Misconception: Voltage is something that "flows" through a wire, similar to current. Why it's wrong: Voltage is a potential difference — a property that exists between two points, not something that physically moves through a conductor. Current is what flows; voltage is what drives it. Correct understanding: Think of voltage like the height difference between two points on a hill and current like the flow of water down that hill. The height difference doesn't "flow" — it's the water that flows, driven by the height difference.

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Misconception: Electric field and electric potential are just two names for the same thing. Why it's wrong: The electric field (E) is a vector with direction, describing force per unit charge, while electric potential (V) is a scalar with only magnitude, describing energy per unit charge. They are mathematically related (the field is the negative gradient of the potential) but are not interchangeable. Correct understanding: Use electric field when you need direction and force (why a charge accelerates a certain way); use electric potential when you're doing energy or voltage calculations. A uniform potential region has zero electric field even though potential itself isn't zero.

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Misconception: Ohm's Law applies to every electronic component. Why it's wrong: Ohm's Law describes a linear relationship between voltage and current that holds for "ohmic" materials like standard resistors and most metals at constant temperature. Diodes, transistors, and other semiconductor devices have a nonlinear V-I relationship. Correct understanding: For a resistor, doubling voltage doubles current in direct proportion. For a diode, current barely changes at all until you cross its forward voltage threshold (~0.7 V for silicon), then rises very steeply — this nonlinearity is precisely what makes diodes and transistors useful as switches and amplifiers, not just current limiters.

Comparison and Connections

Feature	Resistor	Capacitor	Inductor
Stores or dissipates energy	Dissipates as heat	Stores in electric field	Stores in magnetic field
Unit of key property	Ohms (Ω)	Farads (F)	Henries (H)
Behavior with steady DC	Constant current flows continuously	Blocks current once fully charged	Acts like a plain wire (no opposition)
Behavior with sudden change	No special response	Opposes sudden voltage change	Opposes sudden current change
Typical use	Current limiting, voltage division	Filtering, smoothing, coupling	Filtering, transformers, energy storage in switching supplies

Practice Questions

Recall

1. State Ohm's Law and identify the unit of measurement for each quantity in the equation. Focus on: V = IR; voltage in volts, current in amperes, resistance in ohms.

2. Define electric potential and state whether it is a scalar or vector quantity. Focus on: potential energy per unit charge at a point, measured in volts; it is a scalar quantity, unlike electric field which is a vector.

Understanding

3. Explain why current flows through a circuit, using the concept of potential difference rather than potential at a single point. Focus on: current requires a difference in potential between two points to do work moving charge; a single point's potential alone tells you nothing about whether current will flow there.

4. Why does a capacitor block current once fully charged under a steady DC voltage, while a resistor allows current to flow continuously? Focus on: a capacitor's voltage rises as it accumulates charge until it matches the supply voltage, at which point no further charge moves; a resistor offers constant opposition, so current keeps flowing as long as voltage is applied.

Application

5. A 6 V battery is connected across a 3 Ω resistor. Calculate the current and the power dissipated. Focus on: I = V/R = 6/3 = 2 A; P = VI = 6 × 2 = 12 W (or P = I²R = 4 × 3 = 12 W).

6. A household appliance is rated 1000 W at 230 V. Calculate the current it draws and the effective resistance of the appliance. Focus on: I = P/V = 1000/230 ≈ 4.35 A; R = V/I = 230/4.35 ≈ 52.9 Ω (or R = V²/P = 230²/1000 ≈ 52.9 Ω).

Analysis

7. Compare how a resistor and an inductor each respond to a sudden change in current. Why is this difference important when switching off a relay coil? Focus on: a resistor's current changes instantly with voltage; an inductor opposes any sudden change in current by generating a back-EMF, which can spike to a very high voltage when current is abruptly interrupted — this is why flyback diodes are placed across relay coils.

8. Two identical light bulbs are connected first in series, then in parallel, across the same battery. Analyze which configuration makes the bulbs glow brighter and why, in terms of voltage and current. Focus on: in series, the supply voltage divides between the two bulbs, so each gets less voltage and less power; in parallel, each bulb gets the full supply voltage, drawing full rated current and power, so parallel bulbs glow brighter.

FAQ

Is voltage the same as EMF (electromotive force)? They're closely related but not identical. EMF is the energy per unit charge supplied by a source like a battery before any internal losses. Terminal voltage is what you actually measure across the battery's terminals, which is slightly lower than the EMF due to the battery's own internal resistance causing a voltage drop when current flows.

Why does resistance increase with temperature in most conductors? As a conductor heats up, its atoms vibrate more vigorously, which increases the frequency of collisions between the free electrons carrying current and the atomic lattice. More collisions mean more opposition to electron flow, which shows up as higher resistance. This is why incandescent bulb filaments have much higher resistance when glowing hot than when cold.

What's the practical difference between charge and current? Charge (Q) is a quantity — a fixed amount of "stuff," measured in coulombs. Current (I) is a rate — how much charge passes a point per second, measured in amperes (1 A = 1 coulomb per second). It's the same relationship as distance versus speed: charge is like distance traveled, current is like speed.

Why do field lines never cross? At any single point in space, the electric field has one specific direction and magnitude — it can't point two ways at once. Since field lines represent the direction a test charge would move at each point, two lines crossing would imply two different directions at the same point, which is physically impossible.

Can resistance ever be negative? For ordinary passive components like resistors, no — resistance is always positive, meaning they always dissipate energy rather than supply it. However, certain active devices (like tunnel diodes in specific bias regions) can exhibit "negative differential resistance," where increasing voltage causes current to decrease over a limited range. This is a more advanced, non-ohmic behavior used in specialized oscillator circuits, not something you'll encounter with basic resistors.

Quick Revision

• Electric charge is measured in coulombs; one electron carries about 1.6 × 10⁻¹⁹ C
• Charge is conserved — it cannot be created or destroyed, only transferred or separated
• Electric field (vector, force per unit charge) falls off with the square of distance from the source charge
• Electric potential/voltage (scalar, energy per unit charge) is measured in volts; current flows because of a difference in potential
• Ohm's Law: V = IR — holds for ohmic materials like resistors, not for diodes or transistors
• Power: P = VI, with equivalent forms P = I²R and P = V²/R, measured in watts
• Capacitance (farads) stores energy in an electric field; capacitors block steady DC once fully charged
• Inductance (henries) stores energy in a magnetic field; inductors oppose sudden changes in current and can spike voltage when current is interrupted
• Resistors dissipate energy continuously as heat; capacitors and inductors store energy and can return it to the circuit
• Resistance typically increases with temperature in conductors due to increased electron-lattice collisions
• Series circuits divide voltage between components; parallel circuits give each component the full supply voltage

Related Topics

Prerequisites: Overview of Electronics (page 1) — basic components and terminology; History of Electronics (page 2)

Related Topics: Key Concepts in Electronics (page 4), Ohm's Law applications, series and parallel circuit analysis

Next Topics: Kirchhoff's Laws, AC Circuit Analysis, Semiconductor Devices