Electrical engineering cheat sheet

Ohm’s law

For an ohmic element under the assumed conditions, voltage is proportional to current.

V = IR; 2 A through 5 Ω gives 10 V.

Kirchhoff’s laws

Charge conservation constrains currents at a node; energy conservation constrains voltage changes around a loop.

Sum of currents entering a node equals the sum leaving it.

Electrical power

Power is the rate of energy transfer. In a simple DC resistive circuit, equivalent forms follow from Ohm’s law.

P = VI = I²R = V²/R

Series and parallel

Series elements share a current. Parallel branches share the same pair of connection nodes and therefore the same voltage.

Series resistances add: Req = R₁ + R₂.

Voltage and current references

Choose a voltage polarity and current direction before writing circuit equations. A negative result means that the actual direction is opposite to the chosen reference.

Reference arrows organise the calculation; they do not force the physical current to flow that way.

Capacitors

For an ideal capacitor, charge and voltage are related by Q = CV, and stored energy is ½CV². Capacitance is measured in farads.

A capacitor’s voltage cannot change instantaneously under a finite ideal current.

RC time constant

For a simple first-order resistor–capacitor circuit, τ = RC. After one time constant, a charging response has completed about 63% of its change towards the final value.

1 kΩ × 10 μF = 0.01 s = 10 ms.

RMS and sinusoidal signals

RMS expresses a waveform’s effective squared-average magnitude. For a sine wave only, Vrms = Vpeak/√2; other waveforms have different relationships.

A 10 V peak sine wave has RMS voltage about 7.07 V.

Worked example: resistive power

An ideal 6 Ω resistor carries 2 A. Its voltage drop is IR = 12 V and power is I²R = 24 W. The alternative expression V²/R gives the same result.

Check that each expression uses the same resistor and operating condition.

Common mistake: adding every resistance

Series resistors share current and add directly. Parallel branches share voltage; reciprocal resistances add for ideal resistors in parallel.

Two 10 Ω resistors in parallel have equivalent resistance 5 Ω, not 20 Ω.

Check your understanding

What is the time constant of 2000 Ω and 5 μF?

0.01 s, or 10 ms: 2000 × 5 × 10⁻⁶.

Curriculum connections

Sources