In a series RLC circuit, the impedance Z is given by:
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:
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:
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:
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:
At resonance, XL = XC, leading to the resonant frequency formula f₀ = 1/(2π√LC).
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In a parallel RC circuit, the total admittance Y is given by:
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:
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:
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:
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:
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:
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:
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:
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:
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:
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:
At resonance, XL = XC, so they cancel. Z = R (minimum), and current is maximum.
The equivalent resistance of two resistors in parallel is always:
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:
Norton current is the short-circuit current at the load terminals. IN = VTh/RTh.
The voltage regulation of a source is defined as:
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:
Superposition states that the total response is the linear sum of responses to each independent source acting alone.
