Circuit Analysis, Measurement, and Instrumentation
Circuits, power, and measurement
Begin each problem by fixing a reference: choose a phase voltage, state whether values are rms or peak, and record the sign convention for current. For sinusoidal steady state, convert to phasors and use Z = R + jX; keep inductance as +jX and capacitance as −jX. Complex power per phase is S = V I* = P + jQ, so a lagging power factor means Q is positive and current lags voltage. In a balanced three-phase system, total power is √3 V_LL I_L cosθ; never mix line-to-line voltage with phase current unless you include √3.
Measurement questions test loading and transformation. A voltmeter should have high input impedance and an ammeter low resistance; otherwise the meter changes the circuit. Instrument transformers introduce ratio and burden errors: a CT’s secondary must never be open-circuited while primary current flows, and its connected burden must stay below the rated value to avoid saturation. For power measurement, the two-wattmeter method gives total P as the sum of the readings, but one reading can be negative at low power factor; this is a common trap.
Worked example: a balanced 480 V, three-phase load draws 50 kVA at 0.8 lagging. Line current is I = 50,000/(√3 × 480) = 60.1 A. Real power is 40 kW and reactive power is 30 kvar. Rule of thumb: at 480 V three-phase, 1 kVA is about 1.2 A; at 120 V single-phase, 1 kVA is 8.33 A.