Electronics Fundamentals: Ohm's Law, RC Circuits, Voltage Dividers, and More
Understanding a handful of core relationships in electronics lets you design circuits, troubleshoot problems, and interpret datasheets with confidence. This guide covers the foundational concepts every hobbyist and engineer needs: Ohm's Law, the power relationships, passive component behaviour, and practical wiring considerations.
Ohm's Law and the Power Wheel
Ohm's Law states that the voltage across a resistor equals the current through it multiplied by its resistance:
V = I × R
Rearranging gives I = V / R and R = V / I. Adding power (P = V × I) produces twelve derived relationships between V, I, R, and P — sometimes called the power wheel or Ohm's Law wheel. The Ohm's Law Calculator solves for any unknown given two of the four quantities, and the Electronics Power Wheel (V, I, R, P) shows all twelve relationships at once.
| Given | Find V | Find I | Find R | Find P |
|---|---|---|---|---|
| V, I | — | — | V / I | V × I |
| V, R | — | V / R | — | V² / R |
| I, R | I × R | — | — | I² × R |
| P, R | √(P × R) | √(P / R) | — | — |
LED Series Resistor
An LED must have a current-limiting resistor in series or it will draw excessive current and burn out. The required resistance is:
R = (Vsupply − Vforward) / ILED
For example, a red LED with Vf = 2.0 V driven at 20 mA from a 5 V supply needs R = (5 − 2.0) / 0.020 = 150 Ω. The LED Series Resistor Calculator handles this and reminds you to pick the next standard resistor value upward.
Voltage Divider
Two resistors in series divide a supply voltage into a lower output voltage:
Vout = Vin × R₂ / (R₁ + R₂)
This is used to set reference voltages, bias transistors, and interface sensors to microcontrollers. The Voltage Divider Calculator finds Vout or solves for the resistor values you need.
RC Time Constant
A resistor and capacitor together form an RC circuit that charges or discharges exponentially. The time constant τ is:
τ = R × C
After one time constant the capacitor reaches about 63.2 % of its final voltage; after 5τ it is considered fully charged (99.3 %). The time constant governs filter cut-off frequencies, debouncing circuits, and timer intervals. Use the RC Time Constant Calculator (τ = RC) to find τ or back-calculate component values.
LC Resonant Frequency
An inductor (L) and capacitor (C) together resonate at a frequency where their reactances cancel:
f0 = 1 / (2π √(LC))
This principle underlies radio tuning, filters, and oscillators. The LC Resonant Frequency Calculator solves for f0, L, or C given the other two values.
Worked Example: 555 Timer Astable Circuit
The NE555 in astable mode oscillates between high and low states continuously. The frequency and duty cycle depend on two resistors and a capacitor:
- Charge time (high): tH = 0.693 × (R₁ + R₂) × C
- Discharge time (low): tL = 0.693 × R₂ × C
- Frequency: f = 1.44 / [(R₁ + 2R₂) × C]
With R₁ = 1 kΩ, R₂ = 10 kΩ, C = 10 µF: f = 1.44 / [(1000 + 20 000) × 0.000 01] = 1.44 / 0.21 ≈ 6.86 Hz. The 555 Timer Astable Mode Calculator computes frequency and duty cycle for any component combination.
Battery Life and Voltage Drop
Estimating how long a battery will power a circuit is straightforward: hours = capacity (mAh) / current draw (mA). Real-world efficiency losses usually reduce this by 20–30 %. The Battery Life Calculator incorporates a derating factor for a more realistic estimate.
Long wire runs introduce resistance that drops voltage before it reaches the load. The voltage drop across a wire of length L (one-way), cross-sectional resistivity ρ, and current I is Vdrop = 2 × I × ρ × L / A (the factor of 2 accounts for the return conductor). The Voltage Drop Calculator and the Wire Gauge Ampacity Calculator (AWG) help you select wire sizes that keep drop within acceptable limits.
dBm and Signal Power
RF engineers express signal power in dBm — decibels relative to 1 milliwatt: PdBm = 10 × log₁₀(PmW). Going the other way: PmW = 10^(PdBm / 10). Wi-Fi access points typically transmit at 20 dBm (100 mW). Use the dBm to Watts Converter and the Watts to dBm Converter to switch between representations quickly.
Capacitor Energy Storage
A capacitor stores electrostatic energy according to: E = ½CV², where E is in joules, C in farads, and V in volts. A 100 µF capacitor charged to 50 V stores E = 0.5 × 0.0001 × 2500 = 0.125 J. The Capacitor Energy Calculator (E = ½CV²) computes stored energy or the voltage required to reach a target energy level.
Reading Resistor Colour Codes
Through-hole resistors use coloured bands to encode their resistance value. Each colour represents a digit (0–9) and the final band indicates tolerance. The Resistor Color Code Calculator decodes any 4- or 5-band resistor instantly.
Common Mistakes
- Forgetting the return conductor in voltage-drop calculations. Current travels out and back, so total wire length is twice the one-way run.
- Choosing a capacitor voltage rating too close to operating voltage. Always derate by at least 20 % for reliability and safety.
- Ignoring LED forward voltage variation. Red, green, and blue LEDs have different Vf values; do not use the same resistor for all colours on the same supply.
What is the difference between AC and DC power calculations?
For DC circuits, P = V × I directly. For AC circuits, you must account for power factor: Preal = Vrms × Irms × cos(φ). The formulas in this guide apply to DC or to resistive AC loads where power factor equals 1.
How do I choose the right AWG wire gauge?
Select the smallest (highest-numbered) gauge whose ampacity rating exceeds your maximum continuous current, then verify that voltage drop over the run length is within 3–5 % of supply voltage. The Wire Gauge Ampacity Calculator automates both checks.