Electricity Fundamentals

• Charge and currentCurrent is the rate at which charge flows past a point. It is the same everywhere in an unbroken series path — a wire does not 'use up' current. Conventional current flows from + to -, opposite to electron motion; every schematic you will ever read uses the conventional direction.I = Q / t. 1 amp = 1 coulomb per second.
• Voltage is a difference, never an absoluteVoltage is potential energy per unit charge between two points. Asking 'what is the voltage here' is meaningless without a reference. Ground is simply the node you chose to call zero. This single idea prevents most beginner measurement mistakes.V = E / Q. 1 volt = 1 joule per coulomb.
• Resistance and Ohm's lawResistance relates the voltage across a component to the current through it. Ohm's law is a property of resistors, not a law of nature — diodes, LEDs and transistors do not obey it, which is exactly why they are useful.V = I x R. Rearrange to I = V/R and R = V/I.
• Power and heatEvery resistive element converts electrical energy to heat at a rate P = VI. Real parts have a power rating; exceeding it is the most common way beginners destroy components. A 0603 resistor is typically rated 0.1 W, an 0805 0.125 W.P = V x I = I^2 x R = V^2 / R.
• Sources, loads and the closed loopCurrent only flows in a complete loop. An ideal voltage source holds V fixed and lets I be whatever the circuit demands; an ideal current source does the opposite. Real sources have internal resistance, which is why a battery sags under load.Terminal voltage = EMF - I x R_internal.
• Units, prefixes and engineering notationHardware work lives in milli, micro, nano and pico. Get fluent enough that 4k7 (4700 ohm), 100n (100 nF) and 2u2 (2.2 uF) read as fast as words. Engineering notation (exponents in multiples of 3) is how every datasheet and BOM is written.m=1e-3, u=1e-6, n=1e-9, p=1e-12, k=1e3, M=1e6.

ProblemYou have a 5 V supply and a red LED whose datasheet says forward voltage Vf = 2.0 V at a forward current If = 15 mA. Choose a resistor, then check it will not overheat.

1. 1
   The LED and resistor are in series, so the same 15 mA flows through both.
2. 2
   Voltage divides across the loop: 5 V total = 2.0 V across the LED + V_R across the resistor. So V_R = 3.0 V.
3. 3
   Apply Ohm's law to the resistor only: R = V_R / I = 3.0 / 0.015 = 200 ohm.
4. 4
   200 ohm is not an E24 value. The nearest standard values are 180 ohm and 220 ohm. Pick 220 ohm to stay under 15 mA (safer): I = 3.0 / 220 = 13.6 mA.
5. 5
   Check power in the resistor: P = I^2 x R = 0.0136^2 x 220 = 41 mW.
6. 6
   A 0603 resistor rated 100 mW has 2.4x margin. Acceptable.

Answer220 ohm, 0603, 1/10 W. Actual LED current 13.6 mA, resistor dissipation 41 mW.

Tool: Falstad Circuit Simulator (open source, runs in a browser)

• Open the simulator. Delete the default circuit (Edit > Select All, then Delete).
• Draw > Add Voltage Source (2-terminal) and place it vertically. Right-click it, set Voltage to 5 V.
• Draw > Passive Components > Add Resistor. Place it in series. Right-click, set 220 ohm.
• Draw > Outputs and Labels > Add LED. Complete the loop with wires (Draw > Add Wire) back to the source's negative terminal.
• Right-click the negative rail and Add Ground so the simulator has a reference node.
• Hover over each component: the info panel bottom-right shows current, voltage drop and power. Confirm the current matches your hand calculation to within a few percent.
• Change the source to 3.3 V and re-read the current. Recompute by hand first, then check. You should predict the answer before the tool tells you.
• Change the resistor to 22 ohm. Note the LED power. Explain out loud why this destroys the LED.

• DC Electrical Circuit Analysis (Fiore) - Chapters 1 to 2open licencereading~120 minCC BY-NC-SA open textbook. Read chapter 1 (fundamentals, units) and chapter 2 (Ohm's law, power). Do the odd-numbered end-of-chapter problems.
• All About Circuits - Volume I, DC, Chapters 1 to 2freereading~90 minThe clearest plain-English treatment of voltage-as-a-difference anywhere. Free to read online, no account.
• Khan Academy - Electrical Engineering: Circuit analysis basicsfreevideo~60 minUse as a second explanation if the textbook doesn't land. Watch the 'Circuit elements' and 'Ohm's law' sequences only.
• Falstad Circuit Simulatoropen licencetoolGPL-licensed browser simulator with animated current. Source at github.com/pfalstad/circuitjs1. Your sandbox for this whole first block.
• E-series of preferred numbersopen licencereference~10 minSkim the E12 and E24 tables. You will round to these values for the rest of your career.

Design, hand-calculate, simulate and (if you have parts) build a three-LED indicator panel running from a single 5 V supply: one red, one green, one blue LED, each at its own datasheet-recommended current. Every LED must have its own series resistor.

Deliverables

• A one-page calculation sheet showing, for each LED: Vf and If taken from a real datasheet you link to, the resistor value derived from Ohm's law, the chosen E24 value, the resulting actual current, and the resistor power dissipation.
• A Falstad simulation (save via File > Export as Text, or share the generated link) showing all three branches with measured currents annotated.
• A short table comparing your hand-calculated current to the simulated current for each branch, with the percentage error.
• Three sentences explaining why the blue LED needs a different resistor than the red one, even though all three run from the same 5 V.

Acceptance criteria — how you know it is good enough

• Every resistor value is a real E12 or E24 value, not a raw calculator output.
• Every LED current is within 20% of the datasheet recommendation and never above the absolute maximum.
• Hand-calculated and simulated currents agree within 5%.
• The power check is present for every resistor and every result is under 50% of the package rating.

If you want to push further

• Add a fourth branch with two red LEDs in series. Show why this is more efficient than two separate branches, with numbers.
• Recompute the whole panel for a 3.3 V supply and identify which LED can no longer be driven at its rated current. Explain why.

• I can state, without looking it up, what voltage, current, resistance and power each measure and their units.
• Given any two of V, I and R, I can find the third and the power, in under 30 seconds.
• I can explain why 'the voltage at this point' is an incomplete statement.
• I can pick a series resistor for any LED from its datasheet and justify the value chosen.
• I can check a resistor's power dissipation against its package rating and say whether it is safe.
• I read and write 4k7, 100n and 2u2 fluently.