SSC JE Electrical flashcards

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

Bending equation

M/I = σ/y = E/R links bending moment, second moment of area, bending stress, distance from neutral axis, Young's modulus and radius of curvature for elastic bending.

Section modulus Z

For a rectangular section of width b and depth d, Z = bd²/6; the maximum bending stress is M/Z, and a larger Z means lower stress for the same moment.

Euler buckling load

Pcr = π²EI/L² gives the elastic buckling load of a pin-ended column; other end conditions use an effective length factor that replaces L.

Simply supported deflection

A central point load W on span L gives maximum deflection WL³/(48EI); a uniform load w per unit length gives 5wL⁴/(384EI).

Standard consistency of cement

Water content, as a percentage of cement mass, at which the Vicat plunger settles 5–7 mm from the bottom of the mould; used to fix water for setting-time tests.

Slump test

A workability test in which a standard concrete cone is filled and lifted; the vertical settlement of the concrete, in millimetres, indicates consistency.

Rise and fall method

Levelling reduction where rise or fall equals backsight minus foresight; reduced level of next station equals previous reduced level plus rise or minus fall.

Shear stress in beams

τ = VQ/(Ib), where Q is the first moment of area about the neutral axis; for a rectangle the maximum is 3V/(2bd) at the neutral axis.

Fixed-end moment

The moment at a fixed support of a fully restrained beam; for a central point load W on span L each end moment is WL/8.

Target mean strength

For concrete mix design, fm = fck + 1.65σ, where fck is characteristic strength and σ the standard deviation, giving about 5% expected failures.

Polytropic process work

For PVⁿ = C, work done is (P₁V₁ − P₂V₂)/(n − 1) for n ≠ 1; when n = 1 the process is isothermal and work is P₁V₁ ln(V₂/V₁).

Carnot efficiency

η = 1 − T₂/T₁ for a reversible engine operating between absolute temperatures T₁ (hot) and T₂ (cold); no real engine between the same limits can exceed it.

Otto cycle efficiency

η = 1 − 1/r^(γ−1), where r is the compression ratio and γ the specific heat ratio; efficiency rises with compression ratio and with γ.

Diesel cycle efficiency

η = 1 − [1/r^(γ−1)]·[(rc^γ − 1)/(γ(rc − 1))], where rc is the cut-off ratio; for the same compression ratio it is lower than the Otto cycle.

Bernoulli's equation

P/ρg + V²/2g + z = constant along a streamline for steady, incompressible, frictionless flow; it expresses conservation of energy per unit weight.

Reynolds number

Re = ρVD/μ compares inertia to viscous forces; pipe flow is generally laminar below about 2000 and turbulent above about 4000.

Darcy–Weisbach head loss

hf = fLV²/(2gD), where f is the friction factor, L the pipe length, V the mean velocity, g acceleration due to gravity and D the pipe diameter.

Steady flow energy equation

For an open system with steady flow, Q − W = Δh + ΔKE + ΔPE per unit mass, where Q and W are heat and work transfers across the boundary.

First law closed system

Q − W = ΔU for a closed system; heat added minus work done by the system equals the change in internal energy, with sign conventions stated.

Cutting speed

V = πDN/1000 m/min, where D is the workpiece or tool diameter in millimetres and N the rotational speed in revolutions per minute.

Tool signature (ASA)

An ordered list of back rake, side rake, end relief, side relief, end cutting edge and side cutting edge angles, plus nose radius, defining a single-point tool geometry.

Series circuit rule

Current is the same through every element and total resistance is the sum of individual resistances; total voltage divides in proportion to resistance.

Parallel circuit rule

Voltage is the same across every branch and total conductance is the sum of branch conductances; total current divides inversely with branch resistance.

Series resonance

At fr = 1/(2π√(LC)) the inductive and capacitive reactances cancel, impedance is purely resistive and minimum, and current is maximum.

AC power relations

Active power P = VI cos φ, reactive power Q = VI sin φ and apparent power S = VI; cos φ is the power factor and S² = P² + Q².

Three-phase power

For a balanced load, P = √3 V_L I_L cos φ, where V_L is line voltage, I_L line current and cos φ the power factor of the load.

Transformer emf equation

E = 4.44 f N Φm gives the rms induced emf in a winding, where f is frequency, N turns and Φm the maximum core flux.

DC shunt motor back emf

Eb = V − IaRa; torque is proportional to flux times armature current, and speed is proportional to Eb divided by flux.

Synchronous speed

Ns = 120f/P, where f is supply frequency and P the number of poles; slip s = (Ns − N)/Ns and rotor frequency equals sf.

Kirchhoff's current law

The algebraic sum of currents entering a node is zero; charge is conserved, so current in equals current out at any instant.

Thevenin's theorem

Any linear two-terminal network can be replaced by Vth in series with Rth, where Vth is the open-circuit voltage and Rth the resistance seen with sources suppressed.