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A 120-volt heat lamp draws 25 amps of current. What is the lamp's resistance?
- A. 96 ohms
- B. 104 ohms
- C. 150 ohms
- D. 4.8 ohms
Correct Answer: D
Rationale: To find the resistance of the lamp, we use Ohm's Law, which states that resistance (R) is equal to voltage (V) divided by current (I), expressed as: R = V / I. Given that the voltage (V) is 120 volts and the current (I) is 25 amps, we substitute these values into the formula: R = 120 V / 25 A = 4.8 ohms. Therefore, the resistance of the lamp is 4.8 ohms. Choice A, 96 ohms, is incorrect as it is not the result of the correct calculation. Choice B, 104 ohms, is incorrect as it does not match the calculated resistance. Choice C, 150 ohms, is incorrect as it is not the correct resistance value obtained through the calculation.
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According to the Clausius inequality, for a cyclic process involving heat transfer between a system and its surroundings at a single constant temperature (T), the following inequality must hold true:
- A. There is no relationship between heat transfer and temperature in a cyclic process.
- B. ∫ dQ/T ≥ 0
- C. ∫ Q/T = constant
- D. ∫ dQ/T ≤ 0
Correct Answer: D
Rationale: The Clausius inequality states that for a cyclic process involving heat transfer at a single constant temperature, the integral of heat transfer divided by temperature (∫ dQ/T) must be less than or equal to zero. This inequality reflects the irreversibility of natural processes. Choice A is incorrect as there is a direct relationship between heat transfer and temperature in the Clausius inequality. Choice B is incorrect because the integral of dQ/T must be less than or equal to zero, not greater than or equal to zero. Choice C is incorrect because the integral of Q/T is not a constant in a cyclic process involving heat transfer at a single constant temperature.
A caterpillar starts moving at a rate of 14 in/hr. After 15 minutes, it is moving at a rate of 20 in/hr. What is the caterpillar's rate of acceleration?
- A. 6 in/hr²
- B. 12 in/hr²
- C. 24 in/hr²
- D. 280 in/hr²
Correct Answer: C
Rationale: Acceleration is the change in velocity over time. The change in velocity for the caterpillar is 20 in/hr - 14 in/hr = 6 in/hr. Since this change occurred over 15 minutes (or 0.25 hours), the acceleration can be calculated as (6 in/hr) / (0.25 hr) = 24 in/hr². Therefore, the caterpillar's rate of acceleration is 24 in/hr², which corresponds to choice C. Choice A, 6 in/hr², is incorrect as it does not account for the time factor and the correct calculation. Choice B, 12 in/hr², is incorrect as it doubles the correct acceleration value. Choice D, 280 in/hr², is significantly higher than the correct value, indicating a calculation error.
When two long, parallel wires carry currents in the same direction, the wires will experience a force of:
- A. An unpredictable force depending on wire material
- B. Repulsion
- C. No force
- D. Attraction
Correct Answer: D
Rationale: When two wires carry current in the same direction, they create magnetic fields that interact with each other. This interaction results in an attractive force between the wires due to the alignment of their magnetic fields. Choice A is incorrect because the force can be predicted based on the direction of the currents and the magnetic fields produced. Choice B is incorrect because when currents flow in the same direction, they do not repel each other. Choice C is incorrect because there is indeed a force present due to the interaction of magnetic fields, resulting in attraction between the wires.
What is the diameter of a loop if its radius is 6 meters?
- A. 6 m
- B. 12 m
- C. 18 m
- D. 36 m
Correct Answer: B
Rationale: The diameter of a loop is calculated by multiplying the radius by 2. Since the radius is 6 meters, the diameter is 6 2 = 12 meters. Therefore, the correct answer is 12 meters. Choice A (6 m) is the radius, not the diameter. Choices C (18 m) and D (36 m) are incorrect as they do not reflect the correct calculation for determining the diameter of a loop.
In the mechanical power equation P = E / t, power is measured in ___________.
- A. ohms
- B. Joules
- C. volts
- D. watts
Correct Answer: D
Rationale: In the mechanical power equation P = E / t, power is measured in watts. Watts are the standard unit of power in the International System of Units (SI), named after the Scottish engineer James Watt. Watts are defined as joules per second, reflecting the rate at which energy is transferred or converted. Ohms (choice A) are the unit of electrical resistance, Joules (choice B) are the unit of energy, and volts (choice C) are the unit of electric potential difference. Therefore, the correct answer is watts as it directly relates to power in the given equation.