In an RLC circuit, which of the following is always used as a vector reference?

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Examoogle · Accepted Answer

Voltage

Explanation: In AC circuit analysis using phasor diagrams, the supply voltage is conventionally chosen as the reference vector (vector at $0^\circ$ phase angle) for parallel circuits. This approach simplifies calculations as the voltage across all components in a parallel RLC circuit remains identical.

Working Principle: Phasor analysis represents sinusoidal quantities as rotating vectors. By fixing the voltage vector at $V = V_m \angle 0^\circ$, we establish a common baseline to measure the phase shift of branch currents $I_R$, $I_L$, and $I_C$. This facilitates the summation of currents using the algebraic method of complex numbers ($I_{total} = I_R + I_L + I_C$).

Key Formulas: $V(t) = V_m \sin(\omega t)$ — representation of voltage as reference; $I = \frac{V}{Z} = \frac{V}{|Z|\angle\phi}$ — relation between reference voltage and current

Key Points: In parallel circuits, voltage is constant across branches, making it the ideal reference.; In series circuits, current is constant, so current is often chosen as the reference.; The choice of reference is a mathematical convenience, not a physical requirement.; Using voltage as reference simplifies the calculation of the total admittance $Y = G + jB$.

Advantages: Simplifies vector addition of branch currents in parallel circuits; Provides a fixed phase origin for time-domain analysis

Disadvantages: Not optimal for series circuits where current should be the reference; Requires conversion between polar and rectangular coordinates

Applications: AC Power system load flow analysis; Phasor measurement units (PMU) calibration; Design of impedance matching networks

Additional Info: While the question states voltage is 'always' the reference, this is standard convention in basic electrical parallel circuit textbooks. In advanced power systems, current is sometimes used as reference, or a specific bus voltage (Swing Bus) is set as the reference.. Option D (Current) is the standard reference for series RLC circuits.

Answer: A is correct — The voltage vector is standardly chosen as the reference ($0^\circ$ phase) in parallel RLC circuits to facilitate simple vector summation of branch currents.

Exam Tip: Always identify if the circuit is series or parallel first; for series circuits, use Current as the reference vector, and for parallel circuits, use Voltage.

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