Circuit
Maximum Power Transfer Theorem: Choose the Load That Takes the Most Power
Every real source has some internal resistance — a battery, an amplifier output, or a whole network reduced to its Thévenin equivalent. If...
Capacitor
RC Low-Pass Filter: Cutoff Frequency and Frequency Response Explained
A resistor and a capacitor in series make the most useful filter in electronics: the RC low-pass filter. It passes low frequencies almost un...
Circuit
Voltage Divider: The Formula, the Loading Effect, and How to Design One
Two resistors in series across a supply give you any smaller voltage you want — that is the voltage divider, the simplest circuit in electro...
Circuit
Kirchhoff's Laws: KCL and KVL in a Two-Loop Circuit — Worked Example
Two laws carry almost all of circuit analysis. Kirchhoff's current law (KCL) says that the currents entering a node add up to the curren...
Circuit
LED Series Resistor: How to Calculate the Right Value and Protect Your LED
An LED is a diode that lights up — but it is also a diode, which means it has almost no resistance of its own once it starts conductin...
Circuit
Norton Equivalent Circuit: Replace Any Network with One Current Source and One Resistor
Thevenin's theorem replaces a network with a voltage source and a series resistor. Norton's theorem does the same job the othe...
Circuit
Superposition Theorem: Solve a Two-Source Circuit Step by Step
When a circuit has two or more independent sources, solving it all at once can get messy. The superposition theorem gives a simpler way: con...
Circuit
Inductor Energy and the RL Time Constant: How Current Builds Up in a Coil
A capacitor resists a change in voltage; an inductor resists a change in current. Connect an inductor to a battery through a resistor and th...
Circuit
Thevenin Equivalent Circuit: Replace Any Network with One Source and One Resistor
Faced with a complicated network of sources and resistors, you do not have to analyse the whole thing every time the load changes. Thévenin...
Circuit
Ohm's Law and Resistors in Series and Parallel: Worked Example
Ohm's law — V = I × R — is the first equation of electrical engineering, and the series and parallel rules for resistors are the second....
Capacitor
RC Time Constant: Capacitor Charging and Discharging Explained
Connect a capacitor to a battery through a resistor and it does not charge instantly — the voltage climbs in a smooth exponential curve, fas...
Diode
Half-Wave Rectifier: How One Diode Turns AC into DC
A half-wave rectifier is the simplest AC-to-DC converter there is: one diode and one load resistor. The diode conducts only during the posit...
AC Machines
Three-Phase Star vs Delta Connections: Line and Phase Voltage and Current
Three-phase loads and sources are connected in one of two ways: star (Y) or delta (Δ). The two connections behave very differently — in star...
AC Machines
Transformer EMF Equation: E = 4.44 f N Φm — Derivation and Worked Example
Every transformer calculation starts from one equation: E = 4.44 f N Φm. It tells you the RMS voltage induced in a winding from the supply f...
BJT
BJT Transistor as a Switch: Base Resistor and Saturation Explained
A bipolar junction transistor (BJT) is usually taught as an amplifier, but in digital circuits, relay drivers and LED drivers it is used as ...
Diode
Full-Wave Bridge Rectifier: How Four Diodes Turn AC into DC
Almost every DC power supply starts with a rectifier — a circuit that turns alternating current into direct current. The full-wave bridge re...
Semiconductor
Zener Diode as a Voltage Regulator: How It Works and How to Choose the Series Resistor
A Zener diode is an ordinary PN junction diode that is deliberately operated in reverse breakdown. While a normal diode would be destroyed b...
Directional Protection
Ring Main Protection with Directional Overcurrent Relays
A ring main feeds load from two directions, so a fault on one section can be fed from either side. Ordinary non-directional overcurrent rela...
Power System Protection
Buchholz Relay: Principle, Alarm, Trip — and Its Limitations
A transformer can develop a slow internal fault — a winding hot spot, a loose connection, insulation breaking down — long before it becomes ...
Distance Protection
Reactance Relay and the R–X Plane: Why Arc Resistance Does Not Fool It
A distance relay measures the impedance to the fault and trips if it falls inside its zone. The trouble is that a fault arc adds resistance,...
Induction Relay
Wattmeter-Type Induction Relay: Construction and IDMT Characteristic
The wattmeter-type induction relay is the classic overcurrent relay — the spinning-disc relay found in substations for decades before digita...