For a transmission line with characteristic impedance Z₀ = 50 Ω and load impedance ZL = 100 Ω, the reflection coefficient is:
A 0.33 B 0.5 C 0.67 D 1.0
Reflection coefficient Γ = (ZL - Z₀)/(ZL + Z₀) = (100 - 50)/(100 + 50) = 150 50 3 1
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?
A 10.31 Ω B 11.45 Ω C 12.63 Ω D 13.82 Ω
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)?
A The voltage across the load terminals when load is connected B The open-circuit voltage across the terminals where load is removed C The voltage drop across the internal resistance D The maximum voltage the source can provide
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?
A 1 J B 2 J C 4 J D 8 J
Energy stored in capacitor = (2 1 2 1
In a three-phase balanced system, if the line voltage is 400V, what is the phase voltage?
A 230.9 V B 231.1 V C 232.3 V D 233.5 V
In a balanced three-phase system, VL = √3 × Vph. Therefore, Vph = VL/√3 = 400/√3 = 1 400
What is the power factor of a circuit with impedance Z = 8 + j6 Ω?
A 0.6 B 0.8 C 0.5 D 0.707
Z = 8 + j6 Ω, |Z| = √(8² + 6²) = √(64 + 36) = 10 Ω. Power factor = cos(φ) = R/|Z| = 10 8
Two identical resistors R are connected in parallel. What is the equivalent resistance?
A 2R B R/2 C √2 R D R
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?
A 63.66 Ω B 636.6 Ω C 6366 Ω D 63660 Ω
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?
A Impedance increases B Impedance decreases and becomes minimum (equal to R) C Impedance becomes zero D Impedance becomes infinite
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:
A Ratio of reactive power to real power B Ratio of resonant frequency to bandwidth C Ratio of impedance to resistance D Ratio of voltage to current
Quality factor Q = f₀/BW = ω₀L/R = 1/(ω₀RC), representing the sharpness of resonance curve
In mesh analysis, what does each mesh equation represent?
A Kirchhoff's current law for each mesh B Kirchhoff's voltage law around each mesh loop C Power dissipation in each mesh D Energy balance in the circuit
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?
A 0.2 m B 0.201 m C 0.335 m D 0.67 m
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:
A P = VI B P = VI cos(φ) C P = V(t)I(t) D P = VI sin(φ)
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?
A 0.005 s B 0.5 s C 5 s D 50 s
Time constant τ = L/R = 0.100 5
In a circuit with current I = 5sin(314t + 30°) A, what is the RMS value of current?
A 5 A B 3.54 A C 2.5 A D 1.77 A
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?
A To find voltage at each node in the circuit B To find current through each branch C To find power dissipation D To find resonant frequency
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?
A 60 W B 64 W C 80 W D 96 W
S = 100 VA, Z = √(8² + 6²) = 10 Ω, Power factor = R/Z = 10 8
In maximum power transfer theorem, the load resistance should be:
A Equal to source internal resistance B Equal to Thevenin equivalent resistance (RTh) C Much larger than source resistance D Much smaller than source resistance
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?
A 450 W B 900 W C 1350 W D 1800 W
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?
A Vs = Vt + Ir B Vs = Vt - Ir C Vt = Vs + Ir D Vt = Vs/I × r
In a real voltage source, terminal voltage Vt = Vs - Ir, hence Vs = Vt + Ir (accounting for voltage drop across internal resistance)
