NETA AC/DC Theory and Circuits 3 — Questions and Answers

Question 1: In a parallel RLC circuit at resonance, the circuit impedance is:

At its minimum value
Equal to the inductive reactance
At its maximum value (Correct answer)
Equal to zero

Correct answer: At its maximum value

In a parallel RLC circuit at resonance, the impedance is at its maximum value, and the line current is at its minimum.

In a parallel RLC circuit, resonance occurs when XL equals XC, just as in a series circuit. However, the effect on impedance is opposite: the parallel combination of L and C presents very high impedance at resonance, so the total circuit impedance is at its maximum. The source current is at its minimum at resonance because the inductor and capacitor exchange energy with each other rather than drawing it from the source.

Question 2: Kirchhoff's Voltage Law (KVL) states that:

The sum of currents entering a node equals the sum leaving
The algebraic sum of all voltages around any closed loop equals zero (Correct answer)
Voltage is proportional to the square of current
The total voltage in a circuit equals the source voltage divided by resistance

Correct answer: The algebraic sum of all voltages around any closed loop equals zero

KVL: The algebraic sum of all voltage drops and rises around any closed loop in a circuit equals zero.

Kirchhoff's Voltage Law (KVL) is based on the conservation of energy and states that the algebraic sum of all electrical potential differences around any closed loop in a network is zero. In practice, voltage rises (sources) are positive and voltage drops (across resistors, inductors, capacitors) are negative, or vice versa depending on sign convention. KVL is essential for circuit analysis and forms the basis for mesh analysis methods used in fault and load flow studies.

Question 3: The impedance of a capacitor at DC (0 Hz) is:

Zero ohms
Equal to the capacitive reactance
Infinite (open circuit) (Correct answer)
Equal to the resistance of the dielectric

Correct answer: Infinite (open circuit)

At DC (zero frequency), XC = 1/(2*pi*f*C). As f approaches zero, XC approaches infinity. A capacitor blocks DC and appears as an open circuit.

Capacitive reactance is given by XC = 1/(2*pi*f*C). As frequency (f) approaches zero (DC), XC approaches infinity, meaning the capacitor acts as an open circuit to DC current. This property is exploited in coupling and bypass capacitors in electronic circuits. In power system testing, this behavior explains why insulation resistance tests (which apply DC) can assess capacitor-like insulation integrity.

Question 4: When resistors are connected in parallel, the total resistance is:

The sum of all individual resistances
Greater than any individual resistance
Less than the smallest individual resistance (Correct answer)
Equal to the average of all individual resistances

Correct answer: Less than the smallest individual resistance

For parallel resistors, 1/R_total = 1/R1 + 1/R2 + ... The total resistance is always less than the smallest individual resistance.

When resistors are connected in parallel, each provides an additional current path. The total resistance formula is 1/R_total = 1/R1 + 1/R2 + 1/R3 + ... This always results in a total resistance smaller than the smallest individual resistance. For two equal resistors R in parallel, the total is R/2. This principle is applied in electrical testing when understanding parallel fault paths, grounding systems, and determining the effect of multiple loads on a circuit.

Question 5: The unit of inductance is the Henry (H), which is defined as:

One volt per ampere
One ohm-second
One volt-second per ampere (Correct answer)
One watt per hertz

Correct answer: One volt-second per ampere

One Henry is defined as the inductance that produces an EMF of 1 volt when the current changes at a rate of 1 ampere per second. So 1 H = 1 V per (A/s) = 1 V*s/A.

The henry (H) is the SI unit of inductance. From the inductor voltage equation v = L(di/dt), rearranging gives L = v divided by (di/dt). When 1 volt is induced by a current change of 1 ampere per second, the inductance is 1 henry: 1 H = 1 V*s/A = 1 ohm*s. Practical inductors in power systems range from microhenries for small components to several henries for large power transformers. Inductance is critical in understanding transformer behavior and fault current levels.

Question 6: In a DC circuit, the total power dissipated can be expressed as P = V squared divided by R. This formula is derived from:

P = V/I combined with V = I*R
P = V*I combined with V = I*R (Ohm's law) (Correct answer)
P = I*R squared
P = V squared times R

Correct answer: P = V*I combined with V = I*R (Ohm's law)

P = V*I and V = I*R together give P = V*(V/R) = V^2/R. Also equivalent is P = I^2*R.

In a DC resistive circuit, power can be calculated three equivalent ways: P = V*I (voltage times current), P = I^2*R (current squared times resistance), or P = V^2/R (voltage squared divided by resistance). All three are derived from Ohm's law (V = I*R) and the basic power equation P = V*I. These formulas are fundamental for sizing conductors, fuses, and circuit breakers, and for calculating losses in electrical equipment during testing and commissioning work.

NETA AC/DC Theory and Circuits 3

In a parallel RLC circuit at resonance, the circuit impedance is: