NETA AC/DC Theory and Circuits 2 — Questions and Answers

Question 1: In a series RLC circuit at resonance, which of the following is true?

Impedance is at its maximum value
Inductive and capacitive reactances are equal and cancel (Correct answer)
Current is at its minimum value
Power factor equals zero

Correct answer: Inductive and capacitive reactances are equal and cancel

At resonance in a series RLC circuit, XL equals XC, so they cancel and the impedance equals only the resistance R, making it minimum. Current is therefore at its maximum.

In a series RLC circuit, resonance occurs when the inductive reactance (XL = 2πfL) equals the capacitive reactance (XC = 1/2πfC). At this frequency, the two reactances cancel each other out, leaving only the resistance in the circuit. The impedance is therefore at its minimum value (Z = R), and the current is at its maximum. Power factor equals 1 (unity) at resonance since the circuit appears purely resistive.

Question 2: Ohm's law states that current in a circuit is:

Directly proportional to resistance and inversely proportional to voltage
Directly proportional to voltage and inversely proportional to resistance (Correct answer)
Equal to the product of voltage and resistance
Independent of voltage when resistance changes

Correct answer: Directly proportional to voltage and inversely proportional to resistance

Ohm's law: I = V/R. Current is directly proportional to voltage and inversely proportional to resistance.

Ohm's law is expressed as I = V/R, where I is current in amperes, V is voltage in volts, and R is resistance in ohms. This means that for a constant resistance, doubling the voltage doubles the current (direct proportionality). Conversely, for a constant voltage, doubling the resistance halves the current (inverse proportionality). This fundamental law applies to linear, resistive elements under steady-state DC conditions.

Question 3: The time constant of an RC circuit is defined as:

The time for the capacitor to fully charge
The time for the capacitor voltage to reach 63.2% of the applied voltage (Correct answer)
The time for current to reach its maximum value
The time for the capacitor to discharge to zero

Correct answer: The time for the capacitor voltage to reach 63.2% of the applied voltage

The RC time constant t = RC is the time for the capacitor to charge to approximately 63.2% (1 - 1/e) of the source voltage.

The time constant of an RC circuit is t = RC (in seconds, when R is in ohms and C in farads). During charging, after one time constant, the capacitor voltage reaches V x (1 - e^-1) = 0.632 x V, or 63.2% of the applied voltage. After five time constants, the capacitor is considered fully charged (greater than 99%). This concept is crucial for understanding transient behavior in electrical circuits during commissioning and testing.

Question 4: In a purely inductive AC circuit, the current:

Leads the voltage by 90 degrees
Lags the voltage by 90 degrees (Correct answer)
Is in phase with the voltage
Leads the voltage by 45 degrees

Correct answer: Lags the voltage by 90 degrees

In a purely inductive circuit, voltage leads current (or current lags voltage) by 90 degrees due to the inductor's property of opposing changes in current.

In a purely inductive AC circuit, the inductor opposes changes in current according to the equation v = L(di/dt). The voltage reaches its peak before the current does, resulting in current lagging voltage by exactly 90 degrees. The mnemonic 'ELI the ICE man' is useful: in an inductor (L), voltage (E) leads current (I). In a capacitor (C), current (I) leads voltage (E). This phase relationship is fundamental to power factor calculations in AC systems.

Question 5: The effective (RMS) value of a sinusoidal AC voltage is approximately what fraction of the peak voltage?

0.5 times the peak voltage
0.637 times the peak voltage
0.707 times the peak voltage (Correct answer)
1.414 times the peak voltage

Correct answer: 0.707 times the peak voltage

The RMS value of a sine wave is Vpeak divided by the square root of 2, approximately 0.707 times Vpeak. This is the value that produces the equivalent heating effect as a DC voltage.

The Root Mean Square (RMS) value of a sinusoidal waveform is Vpeak x (1/sqrt(2)) = 0.7071 x Vpeak. The RMS value represents the equivalent DC value that would deliver the same power to a resistive load. For example, standard US residential voltage is 120 V RMS, which has a peak voltage of about 170 V. Voltmeters typically read RMS values. The average value of a rectified sine wave is 0.637 x Vpeak, which differs from RMS.

Question 6: Power factor in an AC circuit is defined as:

The ratio of reactive power to apparent power
The ratio of real power to apparent power (Correct answer)
The ratio of apparent power to real power
The ratio of real power to reactive power

Correct answer: The ratio of real power to apparent power

Power factor = Real Power (W) / Apparent Power (VA) = cos(angle), where angle is the phase angle between voltage and current.

Power factor (PF) is the ratio of real (active) power in watts to apparent power in volt-amperes: PF = P/S = cos(angle). A power factor of 1.0 (unity) means all power is being converted to useful work. A low power factor (lagging, due to inductive loads, or leading, due to capacitive loads) means more current must flow to deliver the same real power, increasing losses. In electrical testing, measuring power factor of transformers and cables is a key diagnostic test to assess insulation condition.

NETA AC/DC Theory and Circuits 2

In a series RLC circuit at resonance, which of the following is true?