ESE Prelims Electrical key terms

In a linear bilateral network with multiple independent sources, the response in any branch equals the algebraic sum of the responses produced by each source acting alone, with all other independent sources set to zero (voltage sources shorted, current sources opened).

Any linear two-terminal network can be replaced at its terminals by a single voltage source equal to the open-circuit voltage in series with a resistance equal to the network resistance seen with all independent sources deactivated.

A source delivers maximum power to a load when the load resistance equals the source's Thevenin resistance; the efficiency at that condition is only 50 percent, so it is not a maximum-efficiency criterion.

The frequency at which a series or parallel RLC circuit's inductive and capacitive reactances cancel, making the input impedance purely resistive and the current or voltage amplitude extremal; for a series circuit it equals one over two pi root LC.

A dimensionless measure of a resonant circuit's sharpness, equal to resonant frequency divided by the half-power bandwidth; also the ratio of stored energy to energy lost per radian in a reactive element.

A property of a circuit element or system in which the response to a scaled sum of inputs equals the scaled sum of individual responses, i.e. it obeys both superposition and homogeneity; resistors, inductors and capacitors are linear.

The fractional difference between the synchronous speed of the rotating magnetic field and the actual rotor speed of an induction machine, usually expressed as a per-unit value or percentage; it is zero at synchronous speed and one at standstill.

The rotational speed of the stator's rotating magnetic field, equal to 120 times the supply frequency divided by the number of poles; an induction motor always runs slightly below it in motoring mode.

The curve relating electromagnetic torque of an induction motor to slip; torque rises steeply at low slip, peaks at the breakdown slip, then falls as slip approaches one, explaining stable operation on the near-linear low-slip portion.

For a transformer or generator, the rise in secondary terminal voltage when full load is removed, with primary voltage and excitation held constant, expressed as a percentage of rated terminal voltage.

The distortion and weakening of the main field flux in a DC or synchronous machine caused by the magnetic field of current flowing in the armature winding; it shifts the neutral axis and affects commutation and terminal voltage.

The process in a DC machine by which current in a coil is reversed as its commutator segments pass under a brush, briefly short-circuiting the coil; poor commutation causes sparking at the brushes.

A normalization in which every electrical quantity is expressed as a ratio to a chosen base value of the same dimension, chosen so that transformer turns ratios vanish and faults or loads across voltage levels can be compared directly.

A technique that resolves an unbalanced set of three-phase phasors into three balanced sets: positive sequence, negative sequence and zero sequence, allowing unbalanced faults and loads to be analysed with single-phase equivalent circuits.

The maximum prospective short-circuit current or apparent power a network point can deliver into a bolted fault, determined mainly by source and transformer impedances; switchgear must be rated to withstand and interrupt it.

A steady-state power system analysis that computes bus voltage magnitudes and angles plus real and reactive branch flows for specified generation and load, using iterative methods such as Gauss-Seidel or Newton-Raphson.

A graphical stability test for a synchronous machine connected to an infinite bus: the system remains transiently stable if the accelerating area between power-angle curves equals the maximum available decelerating area after a disturbance.

The differential equation relating a synchronous machine's rotor angle acceleration to the net accelerating power divided by its inertia constant, forming the basis of transient stability simulation.

The ratio of the Laplace transform of a system's output to that of its input under zero initial conditions; for linear time-invariant systems it fully characterizes input-output behaviour.

An algebraic test that determines the number of closed-loop poles in the right half of the s-plane from the coefficients of the characteristic polynomial, without factoring it, by examining sign changes in the first column of an array.

A pair of logarithmic frequency-response graphs showing magnitude in decibels and phase in degrees against frequency; asymptotic straight-line approximations make gain and phase margins easy to read off.

The amount by which open-loop gain can be increased before a closed-loop system becomes marginally stable, read as the negative of the open-loop gain in decibels at the phase-crossover frequency where phase equals minus 180 degrees.

The additional phase lag, at the gain-crossover frequency where open-loop magnitude is unity, that would bring the closed-loop system to the stability boundary; a common design target is 45 to 60 degrees.

A diagram marking the roots of the numerator (zeros) and denominator (poles) of a transfer function in the complex s-plane; pole locations indicate stability and dominant response speed.

A current or voltage transformer that scales high currents or voltages down to safe, standard values for measurement and protection relays while isolating the instrument circuit from the primary system.

The total load, expressed in volt-amperes at rated secondary current or voltage, that an instrument transformer must supply to connected meters, relays and leads while staying within its accuracy class.

A four-arm resistive bridge used to measure an unknown resistance by balancing two ratios so that no current flows through the galvanometer; at balance the unknown equals the product of adjacent known arms divided by the opposite arm.

A modified Wheatstone bridge with a second set of ratio arms that eliminates the effect of contact and lead resistance, making it suitable for measuring very low resistances accurately.

An instrument that plots a signal's instantaneous voltage against time on a phosphor screen by deflecting an electron beam; it reveals waveform shape, amplitude, frequency and phase, unlike a digital multimeter.

The condition at the inverting input of an ideal operational amplifier in a negative-feedback configuration, where the input is held at nearly zero volts relative to ground without being physically connected to it.

A high-gain differential voltage amplifier with very high input impedance and low output impedance; external feedback networks set its closed-loop gain and function, such as inverting, non-inverting and integrator configurations.

The algebra of binary variables using AND, OR and NOT operations, with identities such as De Morgan's laws and absorption used to simplify logic expressions before implementing them in gates.

A rectangular grid arranging truth-table minterms so that adjacent cells differ in one variable, allowing groups of ones to be circled and read off as simplified sum-of-products logic expressions.

A switching technique that controls average output voltage or current by varying the on-time duty ratio of a fixed-frequency square wave, widely used in inverters, choppers and motor drives.

The fraction of each switching period for which a switch or pulse is on, usually expressed as a percentage; in a buck converter the output voltage approximately equals input voltage multiplied by duty cycle.

A four-layer thyristor that conducts anode-to-cathode only after a gate pulse and only while forward-biased, then latches on until current falls below the holding value; it is line-commutated.

The principle that a band-limited signal can be reconstructed exactly only if sampled at more than twice its highest frequency; otherwise aliasing folds high frequencies onto low ones.

The discrete-time counterpart of the Laplace transform, mapping a sequence to a function of complex variable z; it converts linear difference equations into algebraic equations for analysis and design of sampled systems.

The cross product of electric and magnetic field intensities, giving the instantaneous power flow per unit area of an electromagnetic wave; its time average yields radiated power density.

Four coupled partial differential equations relating electric and magnetic fields to charge and current distributions, including the displacement-current term that predicts self-sustaining electromagnetic wave propagation.

The distance into a conductor at which current density and field amplitude fall to about 37 percent of their surface values, shrinking as frequency, permeability and conductivity increase.