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UPSC ESE E&T Network Theory Flashcards
51 question-and-answer cards covering Network Theory as it is examined in UPSC ESE E&T. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.
24 sample cards from the Network Theory deck
Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.
Give the Laplace transforms of e^(−at) and sin(ωt).
L{e^(−at)} = 1/(s+a); L{sin(ωt)} = ω/(s²+ω²); and L{cos(ωt)} = s/(s²+ω²).
State the Laplace differentiation property for f'(t).
L{f'(t)} = sF(s) − f(0⁻), and L{f''(t)} = s²F(s) − s·f(0⁻) − f'(0⁻). This incorporates initial conditions directly.
State the Laplace integration property.
L{∫₀ᵗ f(τ)dτ} = F(s)/s.
State the Initial Value and Final Value Theorems of the Laplace transform.
Initial Value: f(0⁺) = lim(s→∞) sF(s). Final Value: f(∞) = lim(s→0) sF(s), valid only if all poles of sF(s) lie in the left half plane (system is stable).
What are the s-domain impedances of R, L, and C (with zero initial conditions)?
Resistor: R; Inductor: sL; Capacitor: 1/(sC).
What conditions (Dirichlet conditions) must a periodic signal satisfy to have a valid Fourier series?
Over one period the function must be single-valued, have a finite number of maxima/minima, a finite number of finite discontinuities, and be absolutely integrable (∫|f(t)|dt finite).
Write the trigonometric Fourier series of a periodic signal f(t).
f(t) = a₀ + Σ[aₙ cos(nω₀t) + bₙ sin(nω₀t)], where a₀ is the average (DC) value, ω₀ = 2π/T, and aₙ, bₙ are the harmonic coefficients.
Which Fourier coefficients vanish for even and for odd functions?
Even function: only cosine terms (bₙ = 0). Odd function: only sine terms (a₀ = 0 and aₙ = 0). Half-wave symmetry: only odd harmonics are present.
Write the exponential (complex) form of the Fourier series and its coefficient.
f(t) = Σ Cₙ e^(jnω₀t), with Cₙ = (1/T)∫_T f(t)e^(−jnω₀t) dt. The Cₙ are generally complex with conjugate symmetry for real signals.
Define the Fourier Transform and its inverse.
F(ω) = ∫_{−∞}^{∞} f(t)e^(−jωt) dt; inverse f(t) = (1/2π)∫_{−∞}^{∞} F(ω)e^(jωt) dω. It extends Fourier analysis to non-periodic (aperiodic) signals.
What is the key difference between the Fourier Series and the Fourier Transform?
The Fourier series represents periodic signals as a discrete sum of harmonics (line/discrete spectrum); the Fourier transform represents aperiodic signals with a continuous spectrum F(ω).
How are the Fourier and Laplace transforms related?
The Fourier transform is the Laplace transform evaluated on the imaginary axis: F(ω) = F(s)|_{s=jω}, valid when the region of convergence includes the jω-axis (i.e., σ = 0).
State Parseval's theorem for a periodic signal.
The average power equals the sum of the powers of its Fourier components: (1/T)∫_T |f(t)|² dt = Σ |Cₙ|² (exponential form), i.e., total power is distributed among the harmonics.
Define the Z-parameters (open-circuit impedance parameters) of a two-port network.
They relate port voltages to port currents: V₁ = Z₁₁I₁ + Z₁₂I₂ and V₂ = Z₂₁I₁ + Z₂₂I₂. Each Zᵢⱼ is found with one port open-circuited (current = 0).
How is Z₁₁ of a two-port measured?
Z₁₁ = V₁/I₁ with I₂ = 0 (output port open-circuited). It is the input driving-point impedance with the output open.
Define the Y-parameters (short-circuit admittance parameters) of a two-port.
They relate port currents to port voltages: I₁ = Y₁₁V₁ + Y₁₂V₂ and I₂ = Y₂₁V₁ + Y₂₂V₂. Each Yᵢⱼ is found with one port short-circuited (voltage = 0).
How is Y₂₁ of a two-port measured?
Y₂₁ = I₂/V₁ with V₂ = 0 (output short-circuited). It is the forward transfer admittance.
Define the hybrid (H) parameters of a two-port network.
V₁ = h₁₁I₁ + h₁₂V₂ and I₂ = h₂₁I₁ + h₂₂V₂. Here h₁₁ is input impedance (V₂=0), h₁₂ reverse voltage gain (I₁=0), h₂₁ forward current gain (V₂=0), h₂₂ output admittance (I₁=0).
Why are h-parameters widely used for transistors (BJTs)?
Because h₁₁ (input impedance) and h₂₁ (forward current gain β) are easily measured with the output short-circuited, and h₁₂, h₂₂ with the input open — matching how transistor characteristics are naturally specified.
Define the transmission (ABCD) parameters of a two-port network.
They relate input port to output port: V₁ = A·V₂ − B·I₂ and I₁ = C·V₂ − D·I₂ (with I₂ taken as flowing out of port 2). A and D are dimensionless, B is impedance (Ω), C is admittance (S).
How are the ABCD parameters individually defined/measured?
A = V₁/V₂ (I₂=0, output open); B = −V₁/I₂ (V₂=0, output short); C = I₁/V₂ (I₂=0, output open); D = −I₁/I₂ (V₂=0, output short).
What is the main advantage of transmission (ABCD) parameters?
For two-ports connected in cascade, the overall ABCD matrix is the matrix product of the individual ABCD matrices, making cascade analysis straightforward.
What is the reciprocity condition expressed in Z, Y, and ABCD parameters?
A reciprocal two-port satisfies Z₁₂ = Z₂₁, Y₁₂ = Y₂₁, h₁₂ = −h₂₁, and for ABCD parameters AD − BC = 1.
What is the symmetry condition for a two-port network in Z, Y, and ABCD parameters?
A symmetrical two-port satisfies Z₁₁ = Z₂₂, Y₁₁ = Y₂₂, and A = D for the transmission parameters.
What this deck covers
The Network Theory deck follows the UPSC ESE E&T Network Theory syllabus — 3 chapters and 11 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 17.0 cards per chapter.
Answers are written to be recallable, not just readable — averaging about 135 characters, which is long enough to carry the reasoning and short enough to say out loud.
A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.
Network Theory flashcards FAQ
How many Network Theory flashcards are in this UPSC ESE E&T deck?
51 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.
Are these UPSC ESE E&T flashcards free?
Yes. The preview here is free to read with no signup, and the full 51-card deck is free inside the Examius app.
What do the Network Theory cards cover?
They follow the UPSC ESE E&T Network Theory syllabus — 3 chapters and 11 topics — so the questions track what is actually examinable.
How should I use these flashcards?
Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.