Engineer Electricity flashcards

38 cards. Read the term and the definition here. The deck at the top of this page is optional.

Thevenin's theorem

Any linear two-terminal network can be replaced by a single voltage source V_th in series with R_th, where V_th is the open-circuit terminal voltage and R_th is the resistance seen with sources suppressed.

Maximum power transfer

A source delivers maximum power to a load when the load resistance equals the source's Thevenin resistance. At that point the transfer efficiency is only 50 percent, so it is not used for power systems.

Series resonance condition

A series RLC circuit resonates when inductive and capacitive reactances are equal, at f = 1/(2π√(LC)). Impedance is then minimum and purely resistive, current is maximum, and the power factor is unity.

RMS value of sine

For a sinusoidal quantity of peak value V_m, the RMS value is V_m/√2, about 0.707 V_m. RMS is the equivalent DC value producing the same heating effect and is the value normally quoted.

Skin depth

The depth at which current density falls to 1/e of its surface value, given by δ = √(2/(ωμσ)). Higher frequency, permeability, or conductivity gives a shallower depth and higher effective AC resistance.

Reflection coefficient

On a transmission line, Γ = (Z_L − Z₀)/(Z_L + Z₀). A matched load gives zero reflection; a short or open circuit gives Γ of −1 or +1, producing total reflection.

Faraday's law of induction

The induced emf in a coil equals the negative rate of change of magnetic flux linkage, emf = −N dΦ/dt. The minus sign expresses Lenz's law: the induced current opposes the change.

Poynting vector

The cross product S = E×H gives the instantaneous power flow per unit area of an electromagnetic wave, measured in watts per square metre. Its time average gives real power density.

Transformer emf equation

The RMS induced emf in a winding is E = 4.44 f N Φ_max, where f is frequency, N the turns, and Φ_max the peak core flux. It links applied voltage, frequency, and core flux.

Induction motor slip

Slip s = (n_s − n_r)/n_s, where n_s is synchronous speed and n_r is rotor speed. Rotor frequency equals s times supply frequency, and slip rises with load.

Open-circuit transformer test

Applying rated voltage to one winding with the other open gives core loss and the magnetizing branch parameters. Because current is small, copper loss is negligible during this test.

Short-circuit transformer test

Applying a reduced voltage to one winding with the other shorted gives copper loss and the series impedance. Core loss is negligible because the applied voltage is low.

Synchronous speed

The speed of the rotating magnetic field, n_s = 120f/p, where f is supply frequency and p is the number of poles. An induction motor always runs slightly below this speed.

Per-unit system

Quantities are expressed as ratios to chosen base values of power and voltage. Per-unit impedance is unchanged across an ideal transformer, simplifying multi-voltage-level calculations.

Surge impedance loading

SIL = V_L²/Z_c, the power a line delivers when its surge impedance terminates it. For overhead lines Z_c is roughly 400 Ω, so SIL is about V_L²/400 MW.

Ferranti effect

On a lightly loaded or open long transmission line, the receiving-end voltage rises above the sending-end voltage because the line's capacitive charging current causes a voltage rise across the series inductance.

Symmetrical components

Unbalanced three-phase phasors are resolved into positive, negative, and zero-sequence sets. Zero-sequence current requires a return path and is blocked by delta-connected windings.

Distance relay zones

Zone 1 covers about 80 percent of the protected line impedance and trips instantaneously. Zone 2 reaches 120 to 150 percent with a time delay, providing backup for the next line section.

Differential protection principle

Currents entering and leaving the protected zone are compared. Equal through-currents cancel, but an internal fault produces a difference current that operates the relay, giving fast selective protection.

Circuit breaker breaking capacity

The maximum symmetrical short-circuit current a breaker can interrupt at rated voltage without damage. Making capacity is higher, because the first asymmetrical peak must also be withstood.

Buck converter voltage ratio

In continuous conduction, the output voltage of a buck converter is V_o = D·V_in, where D is the duty cycle between 0 and 1. The output is always lower than the input.

Thyristor turn-off

A conducting thyristor returns to the blocking state only when its anode current falls below the holding current, which in AC circuits occurs naturally near current zero.

V/f induction motor control

Keeping the voltage-to-frequency ratio constant maintains approximately constant stator flux. Below base speed this gives constant torque; above base speed the voltage is capped and the field weakens.

Six-pulse converter harmonics

A three-phase six-pulse bridge produces characteristic current harmonics of order 6k ± 1, that is the 5th, 7th, 11th, and 13th, with magnitudes roughly inversely proportional to harmonic order.

Second-order percent overshoot

For a standard second-order system, percent overshoot is 100·e^(−ζπ/√(1−ζ²)), where ζ is the damping ratio. A damping ratio of about 0.7 gives less than 5 percent overshoot.

Steady-state error and system type

The number of integrators in the open-loop transfer function defines the system type. Type 0 has finite step error, type 1 zero step error but finite ramp error, type 2 zero ramp error.

Routh-Hurwitz stability criterion

The Routh array of the characteristic polynomial is built, and the number of sign changes in its first column equals the number of right-half-plane roots, indicating instability.

Gain and phase margin

Gain margin is the factor by which gain can rise before the phase reaches −180 degrees. Phase margin is the phase lag at unity gain. Both positive margins indicate a stable closed loop.

Shunt for ammeter range

A low resistance placed in parallel with a meter extends its current range. Its value is R_m/(m−1), where R_m is meter resistance and m is the desired multiplying factor.

Two-wattmeter method

Two wattmeters connected in two lines of a three-phase system give total power as W₁ + W₂. Power factor is derived from the ratio of their difference to their sum.

Current transformer safety

A current transformer secondary must never be open-circuited while primary current flows, because the whole primary current becomes magnetizing current and induces a dangerous high voltage.

Earth-fault loop impedance

The impedance of the path from the fault back to the source through the protective conductor. It must be low enough for the overcurrent device to disconnect within the required time.

TN and TT earthing systems

In TN systems the installation is connected to the source earth through a protective conductor. In TT systems the installation has its own local earth electrode, usually requiring an RCD.

Cable short-circuit withstand

The cable's cross-section must satisfy I²t ≤ k²S², where I is fault current, t is clearing time, S is conductor area, and k depends on conductor and insulation material.

Net present value

The sum of all project cash flows discounted to the present at the required rate of return. A positive NPV means the project adds value and is economically acceptable.

Critical path method

A scheduling technique where the longest path through the network has zero total float and sets the minimum project duration. Delaying any activity on it delays the whole project.

Cost performance index

In earned value management, CPI = EV/AC, where EV is earned value and AC is actual cost. A CPI below 1 indicates the project is spending more than the work earned.

Conflict of interest disclosure

A professional must disclose any financial or personal interest that could bias engineering judgement, and withdraw from decisions where impartiality cannot be demonstrated.