GATE Electrical Engineering Electric circuits Syllabus

Electric circuits syllabus — full chapter and topic list

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

1. 1

   Network elements

   3 topics

   • Ideal voltage and current sources
   • Dependent sources
   • R, L, C, M elements
2. 2

   Network solution methods

   3 topics

   • KCL
   • KVL
   • Node and Mesh analysis
3. 3

   Network Theorems

   4 topics

   • Thevenin’s theorem
   • Norton’s theorem
   • Superposition theorem
   • Maximum Power Transfer theorem
4. 4

   Transient response of dc and ac networks

   2 topics

   • Sinusoidal steady-state analysis
   • Resonance
5. 5

   Two port networks

   3 topics

   • Balanced three phase circuits
   • Star-delta transformation
   • Complex power and power factor in ac circuits

Electric circuits flashcards for GATE Electrical Engineering

19 of 51 cards from the Electric circuits deck — real questions with worked answers.

1. What is an ideal independent voltage source, and what is its defining property?

   An ideal independent voltage source maintains a fixed terminal voltage $V$ regardless of the current drawn through it. It has zero internal resistance, so its $V$-$I$ characteristic is a horizontal line (voltage constant for any current).

2. What is an ideal independent current source, and what is its defining property?

   An ideal independent current source delivers a fixed current $I$ regardless of the voltage across its terminals. It has infinite internal resistance, so its $V$-$I$ characteristic is a vertical line (current constant for any voltage).

3. How is an ideal voltage source treated for short-circuiting (deactivation), and how is an ideal current source treated?

   To deactivate (zero out) an ideal voltage source, replace it with a short circuit ($V = 0$). To deactivate an ideal current source, replace it with an open circuit ($I = 0$).

4. List the four types of dependent (controlled) sources used in circuit analysis.

   Voltage-Controlled Voltage Source (VCVS), Current-Controlled Voltage Source (CCVS), Voltage-Controlled Current Source (VCCS), and Current-Controlled Current Source (CCCS).

5. For each of the four dependent sources, what are the units of the controlling gain constant?

   VCVS gain is dimensionless ($\mu$); CCVS gain is resistance (transresistance, $r$, in $\Omega$); VCCS gain is conductance (transconductance, $g$, in $\text{S}$); CCCS gain is dimensionless (current gain $\beta$).

6. Write the voltage-current relationship for an inductor and a capacitor.

   Inductor: $v_L = L\dfrac{di_L}{dt}$. Capacitor: $i_C = C\dfrac{dv_C}{dt}$.

7. What quantity cannot change instantaneously in an ideal inductor versus an ideal capacitor?

   The current through an inductor cannot change instantaneously (continuity of $i_L$), and the voltage across a capacitor cannot change instantaneously (continuity of $v_C$).

8. What is the energy stored in an inductor and in a capacitor?

   Inductor: $W_L = \dfrac{1}{2}L i^{2}$. Capacitor: $W_C = \dfrac{1}{2}C v^{2}$.

9. What is mutual inductance $M$, and how is the coupling coefficient $k$ defined?

   Mutual inductance $M$ quantifies the EMF induced in one coil due to a changing current in a magnetically coupled coil: $v_2 = M\dfrac{di_1}{dt}$. The coupling coefficient is $k = \dfrac{M}{\sqrt{L_1 L_2}}$, with $0 \leq k \leq 1$.

10. What is the equivalent inductance of two coupled coils in series, for series-aiding and series-opposing connections?

    Series-aiding (fluxes add): $L_{eq} = L_1 + L_2 + 2M$. Series-opposing (fluxes oppose): $L_{eq} = L_1 + L_2 - 2M$.

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

    The algebraic sum of currents entering any node (or closed boundary) is zero: $\sum_{k} i_k = 0$. Equivalently, the sum of currents entering a node equals the sum of currents leaving it. KCL is a consequence of conservation of charge.

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

    The algebraic sum of voltages around any closed loop is zero: $\sum_{k} v_k = 0$. KVL is a consequence of conservation of energy (the electrostatic field is conservative).

13. In a connected network with $n$ nodes and $b$ branches, how many independent KCL and KVL equations exist?

    Independent KCL equations: $n - 1$. Independent KVL (loop) equations: $b - (n - 1) = b - n + 1$.

14. Describe the basic procedure of nodal analysis.

    Select a reference (ground) node; assign node voltages to the remaining $n-1$ nodes; apply KCL at each non-reference node, expressing branch currents in terms of node voltages and conductances; solve the resulting simultaneous equations for the node voltages.

15. What is a supernode, and when is it used in nodal analysis?

    A supernode is formed by enclosing a voltage source (and any elements in parallel with it) that connects two non-reference nodes. KCL is applied to the supernode as a whole, supplemented by the constraint equation relating the two node voltages through the source voltage.

16. Describe the basic procedure of mesh analysis.

    Assign a circulating mesh current to each independent loop (window) of a planar circuit; apply KVL around each mesh, expressing element voltages in terms of mesh currents and resistances; solve the simultaneous equations for the mesh currents.

17. What is a supermesh, and when is it used in mesh analysis?

    A supermesh is formed when a current source is common to (shared between) two meshes. KVL is written around the combined supermesh excluding the shared source, supplemented by the constraint equation relating the two mesh currents to the source current.

18. 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 sources deactivated).

19. How do you determine the Thevenin resistance $R_{Th}$ of a network?

    Deactivate all independent sources (short voltage sources, open current sources) and compute the equivalent resistance looking into the open terminals. If dependent sources are present, apply a test source $V_{test}$ at the terminals and compute $R_{Th} = \dfrac{V_{test}}{I_{test}}$.

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