Power Systems practice questions

Answer: D) 2 kW

Resistive (copper) loss is P = I²R. Here 100² × 0.2 = 2,000 W, or 2 kW.

• AIncorrect. This comes from dividing current by resistance (100 / 0.2), which doesn't correspond to any power formula.
• BIncorrect. This is I·R = 100 × 0.2 = 20, which is the voltage drop in volts, not power. The current must be squared.
• CIncorrect. This comes from I²/R = 10,000 / 0.2 = 50,000 W. Resistance should multiply, not divide.
• DCorrect. P = I²R = (100 A)² × 0.2 Ω = 10,000 × 0.2 = 2,000 W = 2 kW.

Answer: A) 57.7%

• ACorrect. It's \(1/\sqrt{3}\) of the three-transformer rating.
• BIncorrect. The usable share is lower.
• CIncorrect. It can't match a full bank.
• DIncorrect. That's one transformer's share.

Answer: D) Swap any two of the three supply leads

• AIncorrect. That changes speed, not direction.
• BIncorrect. That keeps the same sequence.
• CIncorrect. Induction motors have no DC field.
• DCorrect. That reverses the phase sequence.

Answer: C) 0.80 lagging

Apparent power is S = √(P² + Q²) = 15 kVA, so PF = P/S = 0.80. It is lagging because the load is inductive.

• AIncorrect. 9/15 = 0.60 is Q/S (the sine of the power-factor angle), not P/S.
• BIncorrect. 9/12 = 0.75 is Q/P, which is tan θ, not cos θ.
• CCorrect. S = √(12² + 9²) = 15 kVA, so PF = P/S = 12/15 = 0.80. It is lagging because the load is inductive and absorbs reactive power.
• DIncorrect. The size is right, but an inductive load absorbs reactive power, so current lags voltage and the power factor is lagging.

Answer: A) 2.8%

• ACorrect. (1,800 − 1,750)/1,800.
• BIncorrect. Divide by synchronous speed.
• CIncorrect. That's speed as a fraction of synchronous.
• DIncorrect. Recheck the calculation.

Answer: D) 1,200 rpm

• AIncorrect. That's for 12 poles.
• BIncorrect. That's for 2 poles.
• CIncorrect. That's for 4 poles.
• DCorrect. \(N_s = 120f/P\).

Answer: D) 36.9°

• AIncorrect. That isn't the conversion.
• BIncorrect. That's \(\cos^{-1}(0.6)\).
• CIncorrect. That isn't the conversion.
• DCorrect. \(\cos^{-1}(0.8)\).

Answer: C) Overvoltages such as lightning or switching surges

• AIncorrect. That's corrected with capacitors.
• BIncorrect. That's overcurrent protection.
• CCorrect. They divert surge current to ground.
• DIncorrect. That uses other protection.

Answer: B) The device closest to the fault operates first, and upstream devices act as time-delayed backup

Coordination (selectivity) grades device settings so the device nearest the fault clears it first and upstream devices serve only as backup. This keeps the outage as small as possible.

• AIncorrect. If adjacent zones trip together, healthy parts of the system lose power for no reason. Coordination is meant to prevent exactly that.
• BCorrect. Selective coordination isolates only the faulted section. Upstream devices are set with enough time margin to trip only if the nearest device fails.
• CIncorrect. This reverses the intended order. Tripping the upstream device first cuts power to every feeder it supplies, not just the faulted one.
• DIncorrect. With identical settings there is no time margin between devices, so they can't be selective. Coordination needs graded pickup and time-delay settings.

Answer: C) It sends a trip signal to a breaker once current goes above its pickup

An overcurrent relay compares measured current with its pickup setting. When the current goes above it, usually after a coordinated time delay, the relay signals a circuit breaker to open. The relay never interrupts current itself.

• AIncorrect. That describes a fuse. A protective relay is a sensing and decision device. It does not interrupt current itself; a circuit breaker does that.
• BIncorrect. That describes a current-limiting reactor. A reactor lowers the fault current but does not detect the fault or isolate the faulted section.
• CCorrect. The relay senses current, usually through a current transformer. When the current goes above the pickup setting, often after an inverse-time delay used for coordination, it energizes the breaker trip circuit and the breaker opens.
• DIncorrect. That describes a reverse-power (directional power) relay, which detects motoring of a generator rather than overcurrent.