For a transmission line with characteristic impedance Z₀ = 50 Ω and load impedance ZL = 100 Ω, the reflection coefficient is:
Reflection coefficient Γ = (ZL - Z₀)/(ZL + Z₀) = (100 - 50)/(100 + 50) = 15050 = 31 ≈ 0.33.
A resistor of 10 Ω is connected in series with an inductor of 0.1 H across a 50 Hz AC supply. What is the impedance of the circuit?
Impedance Z = √(R² + (ωL)²) where ω = 2πf = 2π(50) = 314.16 rad/s. XL = ωL = 314.16 × 0.1 = 31.416 Ω. Z = √(10² + 31.416²) = √(100 + 987.96) = √1087.96 = 32.98 Ω. Correction: XL = 2π × 50 × 0.1 = 31.416 Ω, Z = √(100 + 987.96) ≈ 12.63 Ω is for series RL with proper calculation.
In Thevenin's theorem, what is the Thevenin equivalent voltage (VTh)?
Thevenin equivalent voltage is the open-circuit voltage measured across the two terminals when the load is removed from the circuit.
A capacitor of 100 μF is charged to 200V. What is the energy stored in it?
Energy stored in capacitor = (21)CV² = (21) × 100×10⁻⁶ × 200² = 0.5 × 100×10⁻⁶ × 40000 = 2 J
In a three-phase balanced system, if the line voltage is 400V, what is the phase voltage?
In a balanced three-phase system, VL = √3 × Vph. Therefore, Vph = VL/√3 = 400/√3 = 1400.732 = 230.9 V
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What is the power factor of a circuit with impedance Z = 8 + j6 Ω?
Z = 8 + j6 Ω, |Z| = √(8² + 6²) = √(64 + 36) = 10 Ω. Power factor = cos(φ) = R/|Z| = 108 = 0.8 (lagging)
Two identical resistors R are connected in parallel. What is the equivalent resistance?
For parallel resistors: 1/Req = 1/R + 1/R = 2/R. Therefore, Req = R/2
In a purely capacitive circuit with V = 100V (RMS) and C = 50 μF at 50 Hz, what is the capacitive reactance?
Capacitive reactance XC = 1/(ωC) = 1/(2πfC) = 1/(2π × 50 × 50×10⁻⁶) = 1/(0.0157) = 636.6 Ω
What happens to the impedance of a series RLC circuit when frequency approaches resonant frequency?
At resonance, XL = XC, so Z = √(R² + (XL - XC)²) = R (minimum). This occurs at f₀ = 1/(2π√LC)
The Q-factor of a resonant circuit is defined as:
Quality factor Q = f₀/BW = ω₀L/R = 1/(ω₀RC), representing the sharpness of resonance curve
In mesh analysis, what does each mesh equation represent?
Mesh analysis applies Kirchhoff's voltage law (KVL) around each independent mesh loop in the circuit
A 50 Ω transmission line has a velocity factor of 0.67. What is the wavelength at 1 GHz?
Velocity of propagation v = c × vf = 3×10⁸ × 0.67 = 2.01×10⁸ m/s. Wavelength λ = v/f = 2.01×10⁸/10⁹ = 0.201 m
The instantaneous power in an AC circuit is given by:
Instantaneous power is the product of instantaneous voltage and current: p(t) = v(t)i(t). Average power is VI cos(φ)
What is the time constant (τ) of an RL circuit with R = 100 Ω and L = 0.5 H?
Time constant τ = L/R = 0.1005 = 0.005 s = 5 ms
In a circuit with current I = 5sin(314t + 30°) A, what is the RMS value of current?
For sinusoidal current I = Im sin(ωt + φ), IRMS = Im/√2 = 5/√2 = 3.54 A
What is the purpose of nodal analysis in circuit theory?
Nodal analysis uses Kirchhoff's current law (KCL) at each node to find node voltages, with one node taken as reference (ground)
A circuit has resistance R = 8 Ω and reactance X = 6 Ω (inductive). If the apparent power is 100 VA, what is the real power?
S = 100 VA, Z = √(8² + 6²) = 10 Ω, Power factor = R/Z = 108 = 0.8, Real power P = S × pf = 100 × 0.8 = 80 W
In maximum power transfer theorem, the load resistance should be:
Maximum power transfer occurs when RL = RTh (conjugate of source impedance), delivering Pmax = VTh²/(4RTh)
A sinusoidal voltage v(t) = 300sin(100πt) V is applied to a 50 Ω resistor. What is the average power dissipated?
Vm = 300 V, VRMS = 300/√2 = 212.13 V, P = VRMS²/R = (212.13)²/50 = 900 W
What is the relationship between source voltage (Vs), terminal voltage (Vt), and current (I) in a real voltage source with internal resistance r?
In a real voltage source, terminal voltage Vt = Vs - Ir, hence Vs = Vt + Ir (accounting for voltage drop across internal resistance)
