In a series RLC circuit, the impedance Z is given by:
A Z = √(R² + (XL - XC)²) B Z = R + XL + XC C Z = √(R² + XL² + XC²) D Z = R + √(XL - XC)
Impedance in a series RLC circuit is the vector sum of resistance and net reactance. Z = √(R² + (XL - XC)²) is the standard formula.
The power factor of an AC circuit is defined as:
A cos(φ) where φ is the phase angle between voltage and current B sin(φ) where φ is the phase angle between voltage and current C tan(φ) where φ is the phase angle between voltage and current D 1/cos(φ)
Power factor is the cosine of the phase angle between voltage and current, representing the fraction of apparent power that is real power.
For maximum power transfer in a DC circuit, the load resistance RL should be equal to:
A The Thevenin equivalent resistance RTh B The Norton equivalent current IN C Twice the source resistance D Half the source resistance
Maximum Power Transfer Theorem states that maximum power is delivered when load resistance equals the Thevenin equivalent resistance of the source.
In a purely resistive AC circuit, the phase difference between voltage and current is:
A 0° B 90° C 45° D 180°
In a purely resistive circuit, voltage and current are in phase, so the phase difference is 0°.
The resonant frequency of a series RLC circuit is given by:
A f = 1/(2π√LC) B f = 2π√LC C f = √(LC)/(2π) D f = 1/(√LC)
At resonance, XL = XC, leading to the resonant frequency formula f₀ = 1/(2π√LC).
In a parallel RC circuit, the total admittance Y is given by:
A Y = G + jωC where G = 1/R B Y = G - jωC C Y = √(G² + ω²C²) D Y = G/(1 + ωC)
In a parallel RC circuit, admittances add directly. Y = G + jBC where G = 1/R and BC = ωC.
The Q-factor (quality factor) of a resonant circuit is defined as:
A Q = (1/R)√(L/C) B Q = R√(L/C) C Q = ω₀L/R or 1/(ω₀RC) D Q = R/(ω₀L)
Q-factor represents selectivity and bandwidth characteristics. For series RLC: Q = ω₀L/R = 1/(ω₀RC) = (1/R)√(L/C).
In Thevenin's theorem, the Thevenin equivalent voltage (VTh) is found by:
A Open-circuiting the load and measuring voltage across its terminals B Short-circuiting the load and measuring current C Applying a test voltage at the terminals D Calculating the average voltage across all elements
Thevenin voltage is the open-circuit voltage measured across the load terminals after removing the load.
A capacitor and inductor are in series with resonance occurring at 100 Hz. If L = 25 mH, the capacitance C is approximately:
A 101.3 µF B 50.65 µF C 202.6 µF D 25.3 µF
At resonance: f = 1/(2π√LC). C = 1/(4π²f²L) = 1/(4π²×10000×0.025) ≈ 101.3 µF.
For a node in a circuit applying Kirchhoff's Current Law (KCL), the sum of currents entering equals:
A The sum of currents leaving the node B The voltage at the node C Zero for any configuration D The total power dissipated
KCL states that the algebraic sum of currents at a node is zero, meaning currents entering equal currents leaving.
A bridge circuit is balanced when:
A Z1×Z3 = Z2×Z4 B Z1+Z2 = Z3+Z4 C Z1/Z2 = Z3/Z4 D Z1-Z2 = Z3-Z4
For a balanced AC bridge, the product of opposite arm impedances must be equal: Z1×Z3 = Z2×Z4.
In a purely inductive circuit, the current lags the voltage by:
A 90° B 0° C 45° D 60°
In a purely inductive circuit, current lags voltage by 90° due to self-inductance effects.
The bandwidth of a resonant circuit is related to Q-factor by:
A BW = f₀/Q B BW = Q/f₀ C BW = Q×f₀ D BW = f₀²/Q
Bandwidth is inversely proportional to Q-factor. Higher Q means narrower bandwidth. BW = f₀/Q.
In a delta-wye (Δ-Y) conversion, if the delta resistances are RA, RB, RC, the wye resistance R1 (between node 1 and star point) is:
A (RA×RB)/(RA+RB+RC) B RA+RB+RC C (RA×RC)/(RA+RB+RC) D RA/3
In Δ-Y conversion, each Y-resistor equals the product of adjacent Δ-resistors divided by the sum of all Δ-resistors.
An ideal voltage source has internal resistance of:
A Zero B Infinite C Equal to load resistance D 1 Ω
An ideal voltage source maintains constant voltage regardless of load, which requires zero internal resistance.
In a series RLC circuit at resonance, the impedance is:
A Minimum and equal to R B Maximum and equal to R C Equal to XL + XC D Equal to √(R² + L²)
At resonance, XL = XC, so they cancel. Z = R (minimum), and current is maximum.
The equivalent resistance of two resistors in parallel is always:
A Less than the smaller resistor B Greater than both resistors C Equal to their arithmetic mean D Equal to their sum divided by 2
For parallel resistors: Req = (R1×R2)/(R1+R2), which is always less than the smaller individual resistor.
In Norton's theorem, the Norton equivalent current (IN) is found by:
A Short-circuiting the load terminals and calculating the current through the short circuit B Open-circuiting the load terminals C Removing all independent sources D Calculating Thévenin voltage divided by Thévenin resistance
Norton current is the short-circuit current at the load terminals. IN = VTh/RTh.
The voltage regulation of a source is defined as:
A (VNL - VFL)/VFL × 100%, where VNL is no-load voltage and VFL is full-load voltage B (VFL - VNL)/VNL × 100% C (VNL + VFL)/2 × 100% D VNL/VFL × 100%
Voltage regulation measures the percentage change in output voltage from no-load to full-load conditions.
In a complex circuit using superposition theorem, the total response is found by:
A Adding the responses due to each independent source acting alone B Multiplying individual responses C Taking the average of all responses D Finding the RMS of individual responses
Superposition states that the total response is the linear sum of responses to each independent source acting alone.
