TN LLE Electrical Theory 2 — Questions and Answers
Question 1: In a series circuit with three resistors of 10 ohms, 20 ohms, and 30 ohms connected to a 120V source, what is the total current?
- 2 amperes (Correct answer)
- 4 amperes
- 6 amperes
- 12 amperes
Correct answer: 2 amperes
Total resistance in series = 10 + 20 + 30 = 60 ohms. Current = V/R = 120/60 = 2 amperes.
In a series circuit, total resistance is the sum of individual resistances: Rtotal = R1 + R2 + R3 = 10 + 20 + 30 = 60 ohms. Using Ohm's law, I = V/Rtotal = 120V/60 ohms = 2 amperes. In a series circuit, the same current flows through every component. The voltage drops across each resistor would be: V1 = 2A x 10 ohms = 20V, V2 = 2A x 20 ohms = 40V, V3 = 2A x 30 ohms = 60V. The sum of voltage drops (20 + 40 + 60 = 120V) equals the source voltage, confirming Kirchhoff's voltage law.
Question 2: What is the power consumed by a 240V electric water heater drawing 20 amperes?
- 2,400 watts
- 4,800 watts (Correct answer)
- 1,200 watts
- 960 watts
Correct answer: 4,800 watts
Power = Voltage x Current = 240V x 20A = 4,800 watts (4.8 kW).
The power formula P = V x I gives us: P = 240V x 20A = 4,800 watts or 4.8 kW. This is a common water heater rating. To convert to kilowatt-hours for energy consumption, a 4,800W heater running for 1 hour consumes 4.8 kWh. Per NEC, this 4,800W, 240V load requires a minimum 10 AWG conductor on a 30A circuit (since it's a continuous load: 20A x 125% = 25A minimum).
Question 3: What is the power factor in a purely resistive AC circuit?
- 0
- 0.5
- 0.8
- 1.0 (Correct answer)
Correct answer: 1.0
In a purely resistive circuit, voltage and current are in phase, resulting in a power factor of 1.0 (unity).
Power factor is the cosine of the phase angle between voltage and current. In a purely resistive circuit, there is no phase difference (angle = 0 degrees), so PF = cos(0) = 1.0. This means all power delivered is real (useful) power. In circuits with inductance (motors, transformers), current lags voltage, reducing the power factor below 1.0. A PF of 0.8 means only 80% of the apparent power is doing useful work. Power factor correction capacitors can be added to improve PF, reducing utility costs for commercial customers.
Question 4: Two 100 ohm resistors connected in parallel have a combined resistance of:
- 200 ohms
- 100 ohms
- 50 ohms (Correct answer)
- 25 ohms
Correct answer: 50 ohms
For two equal resistors in parallel: Rtotal = R/2 = 100/2 = 50 ohms.
For parallel resistors, 1/Rtotal = 1/R1 + 1/R2 = 1/100 + 1/100 = 2/100. Therefore, Rtotal = 100/2 = 50 ohms. A quick rule: for two equal resistors in parallel, the total is always half of one resistor's value. For unequal resistors, use the product-over-sum formula: Rtotal = (R1 x R2)/(R1 + R2). Parallel resistance is always less than the smallest individual resistor. This principle is important for understanding why adding parallel loads to a circuit increases total current draw.
Question 5: What is the relationship between voltage, current, and resistance known as?
- Kirchhoff's law
- Ohm's law (Correct answer)
- Faraday's law
- Watt's law
Correct answer: Ohm's law
Ohm's law (V = I x R) describes the fundamental relationship between voltage, current, and resistance.
Ohm's law, expressed as V = I x R (voltage equals current times resistance), is the foundation of electrical theory. It can be rearranged to find any value: I = V/R (current), R = V/I (resistance). Georg Simon Ohm published this relationship in 1827. Combined with Watt's law (P = V x I), these formulas allow calculation of any electrical quantity. For Tennessee LLEs, Ohm's law is essential for load calculations, voltage drop calculations, conductor sizing, and troubleshooting.
Question 6: In a 120/240V single-phase residential service, what voltage exists between the two hot conductors?
- 120 volts
- 208 volts
- 240 volts (Correct answer)
- 480 volts
Correct answer: 240 volts
In a 120/240V single-phase system, the two hot (ungrounded) conductors are 240 volts apart, each being 120 volts to the neutral.
A 120/240V single-phase residential service uses a center-tapped transformer. Each hot conductor (L1 and L2) is 120V to the center tap (neutral). Since L1 and L2 are 180 degrees out of phase, the voltage between them adds up: 120V + 120V = 240V. This is why 240V circuits use both hot conductors but may not require a neutral (like a water heater or A/C compressor), while 120V circuits use one hot and the neutral. This is the most common residential service configuration in Tennessee and throughout the United States.
TN LLE Electrical Theory 2
In a series circuit with three resistors of 10 ohms, 20 ohms, and 30 ohms connected to a 120V source, what is the total current?