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Electrical Science Formula Reference
Organised by the question you are solving: quantity, power, network, conductor model, waveform or force. Check the stated conditions before using a formula.
Technical review pending. This independently reorganised reference is not currently approved for commercial-course use. It is a study aid, not a design or safe-working instruction. It is not an official awarding-body resource.
Start with the quantity you need
A compact task-first index. Check units and assumptions before using any relationship.
- Current: I = Q / t
- Average current over the stated interval; A = C/s
- Charge: Q = I × t
- Constant current, or interval-average current; time in seconds, Q in coulombs
- Voltage: V = E / Q
- Energy transferred per unit charge; J/C
- Resistance model: R = V / I
- For the stated operating conditions
- Ohm's law: V = I × R
- Ohmic element under constant physical conditions
Find power and energy
Choose only a relationship whose assumptions match the circuit.
- DC power: P = V × I
- Power in watts
- Resistive power: P = I² × R
- Ideal resistive/DC model
- Resistive power: P = V² / R
- Ideal resistive/DC model
- Energy: E = P × t
- Constant or interval-average power; W·s gives joules, kW·h gives kWh
- Efficiency = useful output / input
- Multiply by 100 for percent
Compare network arrangements
Sketch the nodes first; series and parallel describe topology, not visual orientation.
- Series resistance: Rtotal = ΣR
- Same current through one path
- Series loop: Vsource = ΣVdrop
- Ideal closed-loop model
- Parallel conductance: 1/Rtotal = Σ(1/Ri)
- Equivalent resistance follows by inversion
- Two parallel resistors: Rtotal = R1R2/(R1+R2)
- Only for two resistors
- Parallel node: Itotal = ΣIbranch
- Current balance at a node
Estimate conductor-model changes
Use consistent SI units; this relation is not a cable-selection rule.
- Uniform conductor: R = ρL/A
- ρ in Ω·m, L in m, A in m²
- Convert area: A(m²) = A(mm²) / 1,000,000
- Because 1 mm = 0.001 m
- Scale: R ∝ L
- At fixed material, area and temperature
- Scale: R ∝ 1/A
- At fixed material, length and temperature
- Loop path: include outgoing and return conductors
- When modelling a complete two-conductor loop
Read periodic signals
The common factors below apply to a pure sinusoid only.
- Frequency: f = 1/T
- f in hertz; T in seconds
- Sine-wave RMS: Vrms = Vpeak / √2
- Approximately 0.707 × peak
- Sine-wave peak: Vpeak = √2 × Vrms
- Approximately 1.414 × RMS
- Sine-wave peak-to-peak = 2 × peak
- For a symmetrical waveform
- Full-cycle average of symmetrical sine = 0
- Half-cycle average is a separate quantity
Connect field, force and motion
Idealised relationships; direction and geometry matter.
- Flux density: B = Φ/A
- Uniform field perpendicular to area
- Induced voltage magnitude: E = Bℓv
- Uniform-field model: straight effective conductor length, velocity and magnetic field mutually perpendicular
- Conductor force: F = B I ℓ
- Current and field perpendicular
- Mechanical work: W = Fd
- Force and displacement in same direction
- Mechanical power: P = W/t
- For steady force and speed, P = Fv
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