GATE EE Formula Sheet for Quick Revision
GATE Electrical Engineering important formulas on one page: circuits, fields, signals, machines, power systems, control, measurements and power electronics.
The formulas that GATE Electrical Engineering numerical questions use most, subject by subject. Use this page for revision after studying each lesson.
Electric circuits
| Formula | Meaning |
|---|---|
| τ = RC or L/R | Time constant of first-order circuits |
| ω₀ = 1/√(LC), Q = ω₀L/R (series) | Resonance and quality factor |
| P = VI cos φ, Q = VI sin φ, S = VI | Real, reactive and apparent power (RMS values) |
| Maximum power transfer: R_L = R_th (Z_L = Z_th* for AC) | Load matching |
| Star–delta: R_Y = R_Δ/3 (balanced) | Conversion |
See Electric circuits.
Electromagnetic fields
| Formula | Meaning |
|---|---|
| F = q₁q₂/(4πε₀r²) | Coulomb's law |
| C = εA/d | Parallel-plate capacitor |
| L = μN²A/l | Inductance of a long solenoid |
| ∮ H·dl = I_enclosed | Ampere's law |
Signals and systems
| Formula | Meaning |
|---|---|
| f_s ≥ 2 f_max | Nyquist sampling rate |
| y(t) = x(t) * h(t) | Output of an LTI system is the convolution with the impulse response |
| Stable (causal LTI) | All poles in the left half s-plane, or inside the unit circle in z |
See Signals and systems.
Electrical machines
| Formula | Meaning |
|---|---|
| V₁/V₂ = N₁/N₂ = I₂/I₁ | Ideal transformer |
| Max efficiency when copper loss = core loss | Transformer |
| N_s = 120f/P | Synchronous speed (rpm) |
| s = (N_s − N)/N_s | Slip of an induction motor |
| E = PφNZ/(60A) | EMF of a DC machine |
| Rotor copper loss = s × air-gap power | Induction motor power flow |
See Electrical machines.
Power systems
| Formula | Meaning |
|---|---|
| P = (V₁V₂/X) sin δ | Power transfer over a lossless line |
| Per-unit: Z_pu = Z × S_base/V_base² | Per-unit impedance |
| Z_new = Z_old × (V_old/V_new)² × (S_new/S_old) | Change of base |
| Fault current (3-phase, pu) = 1/Z_th | Symmetrical fault |
See Power systems.
Control systems
| Formula | Meaning |
|---|---|
| T(s) = G/(1 + GH) | Closed-loop transfer function |
| Second order: ω_n² / (s² + 2ζω_n s + ω_n²) | Standard form |
| Peak overshoot M_p = e^(−πζ/√(1 − ζ²)) | Step response |
| Settling time (2%) ≈ 4/(ζω_n) | Step response |
| e_ss (step) = 1/(1 + K_p), (ramp) = 1/K_v | Steady-state error |
See Control systems.
Measurements and power electronics
| Formula | Meaning |
|---|---|
| Shunt R_sh = I_m R_m/(I − I_m) | Ammeter range extension |
| Two-wattmeter: tan φ = √3 (W₁ − W₂)/(W₁ + W₂) | Balanced three-phase power factor |
| Buck: V_o = D V_in; boost: V_o = V_in/(1 − D) | DC–DC converters |
| Single-phase full converter: V_o = (2V_m/π) cos α | Controlled rectifier |
See Measurements and Power electronics.
Check yourself
A 4-pole, 50 Hz induction motor runs at 1440 rpm. What is its slip?
Show answer and explanation
Answer: 0.04N_s = 120 × 50/4 = 1500 rpm; s = (1500 − 1440)/1500 = 0.04.
A buck converter has input 48 V and duty ratio 0.25. What is the output voltage in V?
Show answer and explanation
Answer: 12V_o = D V_in = 0.25 × 48 = 12 V.
A second-order system has ζ = 0.5 and ω_n = 4 rad/s. What is the 2% settling time in seconds?
Show answer and explanation
Answer: 2t_s ≈ 4/(ζω_n) = 4/2 = 2 s.
A series RLC circuit has L = 10 mH and C = 100 µF. What is the resonant angular frequency in rad/s?
Show answer and explanation
Answer: 1000ω₀ = 1/√(LC) = 1/√(10⁻⁶) = 1000 rad/s.
A signal has highest frequency 4 kHz. What is the minimum sampling rate in kHz?
Show answer and explanation
Answer: 8Nyquist rate = 2 × 4 = 8 kHz.