GATE Electrical Engineering (EE) Syllabus

Electrical Engineering (EE) syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Electrical Engineering (EE) in GATE, not a summary of it.

1. 1

   Electric Circuits and Networks

   4 topics

   • Circuit Analysis Techniques
     • KCL, KVL and nodal/mesh analysis
     • Thevenin, Norton and superposition
   • Transient and Steady-State Response
     • RL, RC and RLC circuits
   • AC Circuit Analysis
     • Phasors and power factor
     • Resonance and three-phase circuits
   • Two-Port Networks and Theorems
2. 2

   Electromagnetic Fields

   3 topics

   • Electrostatics
     • Coulomb's and Gauss's laws
     • Capacitance and dielectrics
   • Magnetostatics
     • Ampere's and Biot-Savart laws
     • Inductance
   • Time-Varying Fields
     • Faraday's law and Maxwell's equations
3. 3

   Electrical Machines and Power Systems

   4 topics

   • Transformers
     • Equivalent circuit and efficiency
     • Three-phase transformer connections
   • DC and AC Machines
     • DC motors and generators
     • Induction and synchronous machines
   • Power System Analysis
     • Transmission line parameters and performance
     • Load flow and fault analysis
   • Power System Protection and Stability
     • Circuit breakers and relays
4. 4

   Control Systems

   4 topics

   • System Modeling and Transfer Functions
     • Block diagrams and signal flow graphs
   • Time and Frequency Response
     • Transient and steady-state error
     • Bode and Nyquist plots
   • Stability Analysis
     • Routh-Hurwitz criterion
     • Root locus
   • Compensators and State-Space Analysis
5. 5

   Power Electronics and Measurements

   4 topics

   • Power Semiconductor Devices
     • Diodes, BJTs, MOSFETs and thyristors
   • Converters
     • Rectifiers and choppers
     • Inverters and AC voltage controllers
   • Electrical Measurements
     • Bridges and potentiometers
     • Measurement of voltage, current and power
   • Analog and Digital Instrumentation

Electrical Engineering (EE) flashcards for GATE

24 of 51 cards from the Electrical Engineering (EE) deck — real questions with worked answers.

1. State Kirchhoff's Current Law (KCL).

   The algebraic sum of all currents entering and leaving any node (junction) is zero: $\sum_{k} i_k = 0$. It expresses conservation of charge — the total current entering a node equals the total current leaving it.

2. State Kirchhoff's Voltage Law (KVL).

   The algebraic sum of all voltages around any closed loop is zero: $\sum_{k} v_k = 0$. It expresses conservation of energy around a loop.

3. In nodal analysis vs. mesh analysis, what variable is solved for in each?

   Nodal analysis solves for node voltages using KCL at each non-reference node. Mesh analysis solves for loop (mesh) currents using KVL around each independent loop. Nodal is preferred when there are more voltage sources/fewer nodes; mesh when there are more current sources/fewer meshes.

4. How do you find the number of independent KCL and KVL equations for a network with $n$ nodes and $b$ branches?

   Independent KCL equations: $n-1$ (one node taken as reference). Independent KVL equations (loops): $b-(n-1) = b-n+1$.

5. State Thevenin's theorem.

   Any linear two-terminal network can be replaced by an equivalent circuit consisting of a single voltage source $V_{th}$ (the open-circuit voltage) in series with a single resistance $R_{th}$ (the equivalent resistance seen from the terminals with independent sources deactivated).

6. State Norton's theorem and its relation to Thevenin's.

   Any linear two-terminal network can be replaced by a current source $I_N$ (the short-circuit current) in parallel with a resistance $R_N$. The two are related by $V_{th} = I_N R_N$ with $R_{th} = R_N$.

7. How do you deactivate independent sources when finding $R_{th}$?

   Replace independent voltage sources with a short circuit and independent current sources with an open circuit. Dependent sources are kept and handled by applying a test source at the terminals: $R_{th} = \frac{V_{test}}{I_{test}}$.

8. State the superposition theorem and its key limitation.

   In a linear network, the response (voltage or current) caused by multiple independent sources equals the algebraic sum of the responses caused by each source acting alone. Limitation: it applies to current and voltage but NOT to power, since power is a nonlinear ($\propto V^2$ or $I^2$) quantity.

9. State the Maximum Power Transfer theorem for a DC source with internal (Thevenin) resistance.

   Maximum power is delivered to the load when $R_L = R_{th}$. The maximum power delivered is $P_{max} = \frac{V_{th}^{2}}{4R_{th}}$, and the efficiency at this point is only $50\%$.

10. For AC circuits, what load impedance maximizes power transfer from a source of impedance $Z_{th} = R_{th} + jX_{th}$?

    The complex conjugate match: $Z_L = Z_{th}^{*} = R_{th} - jX_{th}$. Then $P_{max} = \frac{|V_{th}|^{2}}{8R_{th}}$ (using amplitude) or $\frac{V_{th,rms}^{2}}{4R_{th}}$.

11. Write the time constant for a series RC circuit and an RL circuit.

    RC circuit: $\tau = RC$. RL circuit: $\tau = \frac{L}{R}$. After one time constant the transient quantity reaches about $63.2\%$ of its final change.

12. Write the charging voltage of a capacitor in a series RC circuit driven by a step source $V_s$.

    $$v_C(t) = V_s\left(1 - e^{-t/RC}\right)$$ The capacitor current is $i(t) = \frac{V_s}{R}e^{-t/RC}$.

13. Write the natural (discharge) response of current in a series RL circuit with initial current $I_0$.

    $$i_L(t) = I_0\, e^{-t/\tau}, \quad \tau = \frac{L}{R}$$ The current decays exponentially to zero.

14. What is the general form of a first-order circuit response, and what do its terms represent?

    $$x(t) = x(\infty) + \big[x(0^{+}) - x(\infty)\big]e^{-t/\tau}$$ where $x(\infty)$ is the steady-state (final) value, $x(0^{+})$ is the initial value just after switching, and $\tau$ is the time constant.

15. What are the continuity (boundary) conditions for inductors and capacitors at the instant of switching?

    Inductor current cannot change instantaneously: $i_L(0^{+}) = i_L(0^{-})$. Capacitor voltage cannot change instantaneously: $v_C(0^{+}) = v_C(0^{-})$.

16. For a series RLC circuit, write the resonant (natural undamped) frequency and the damping condition expressions.

    $$\omega_0 = \frac{1}{\sqrt{LC}}$$ Damping ratio $\zeta = \frac{R}{2}\sqrt{\frac{C}{L}}$; neper frequency $\alpha = \frac{R}{2L}$. The response is overdamped if $\alpha > \omega_0$, critically damped if $\alpha = \omega_0$, and underdamped if $\alpha < \omega_0$.

17. Classify the three damping cases of a second-order RLC circuit.

    Overdamped ($\zeta>1$): two distinct real roots, no oscillation, slow return. Critically damped ($\zeta=1$): repeated real root, fastest non-oscillatory return. Underdamped ($\zeta<1$): complex roots, damped oscillation at $\omega_d = \omega_0\sqrt{1-\zeta^{2}}$.

18. Define a phasor and how a sinusoid $v(t) = V_m\cos(\omega t + \phi)$ is represented.

    A phasor is a complex number representing the amplitude and phase of a sinusoid: $\mathbf{V} = V_m\angle\phi = V_m e^{j\phi}$. The time signal is recovered by $v(t) = \text{Re}\{\mathbf{V}e^{j\omega t}\}$.

19. Write the impedances of R, L, and C in phasor (frequency) domain.

    Resistor: $Z_R = R$. Inductor: $Z_L = j\omega L$. Capacitor: $Z_C = \frac{1}{j\omega C} = -\frac{j}{\omega C}$.

20. Define power factor and state when it is leading vs. lagging.

    Power factor $\text{pf} = \cos\theta$, where $\theta$ is the phase angle between voltage and current. It is lagging for an inductive load (current lags voltage) and leading for a capacitive load (current leads voltage).

21. Write the complex power $S$ and its components.

    $$S = VI^{*} = P + jQ$$ where $P = VI\cos\theta$ is real (average) power in watts, $Q = VI\sin\theta$ is reactive power in VAR, and $|S| = VI$ is apparent power in VA. Also $|S| = \sqrt{P^{2}+Q^{2}}$.

22. Define the quality factor $Q$ of a series RLC resonant circuit.

    $$Q = \frac{\omega_0 L}{R} = \frac{1}{\omega_0 R C} = \frac{1}{R}\sqrt{\frac{L}{C}}$$ A higher $Q$ means sharper resonance and a narrower bandwidth.

23. Relate bandwidth, resonant frequency, and quality factor for a resonant circuit.

    $$\text{BW} = \omega_2 - \omega_1 = \frac{\omega_0}{Q} = \frac{R}{L}\ \text{(series RLC)}$$ The bandwidth is the range between half-power (−3 dB) frequencies.

24. At resonance in a series RLC circuit, what happens to the impedance and current?

    Inductive and capacitive reactances cancel ($X_L = X_C$), so impedance is purely resistive and minimum ($Z = R$). The current is maximum and in phase with the source voltage (pf = 1).

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