4.2.4 Resistance (3)
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1.
A student uses a 24V electric iron to heat water. The current through the iron is 3A. Calculate the electrical energy used by the iron in 5 minutes. Express your answer in Joules.
Given:
- Voltage (V) = 24 V
- Current (I) = 3 A
- Time (t) = 5 minutes = 5 x 60 seconds = 300 seconds
Equation:
Electrical Energy (E) = Current (I) x Voltage (V) x Time (t)
Calculation:
E = 3 A x 24 V x 300 s
E = 21600 J
Answer: The electrical energy used by the iron is 21600 J.
2.
A resistor of length 15 cm and cross-sectional area of 2 mm2 has a resistance of 3.0 Ω. If the length of the resistor is doubled, what is the new resistance? (Use the relationships: Resistance is directly proportional to length and inversely proportional to the cross-sectional area.)
Solution:
- Initial resistance formula: R = ρL/A. We know R = 3.0 Ω, L = 0.15 m, and A = 2 x 10-6 m2. We can use this to find the resistivity (ρ): 3.0 Ω = ρ(0.15 m) / (2 x 10-6 m2). Therefore, ρ = (3.0 Ω)(2 x 10-6 m2) / (0.15 m) = 4 x 10-5 Ωm.
- New length: The length is doubled, so the new length (L') is 30 cm = 0.3 m.
- Calculate the new resistance: R' = ρL' / A = (4 x 10-5 Ωm)(0.3 m) / (2 x 10-6 m2) = 0.6 Ω.
Answer: The new resistance is 0.6 Ω.
3.
Describe an experiment to investigate the relationship between the current flowing through a resistor and the amount of heat produced. Include a list of the equipment required, the procedure, and how you would measure the heat produced. Explain what you would expect to observe and why.
Equipment Required:
- Power Supply (variable voltage)
- Resistor (known resistance)
- Ammeter
- Voltmeter
- Thermometer
- Insulated Container (to minimise heat loss)
- Stopwatch
Procedure:
- Set up a circuit with the power supply, resistor, ammeter, and voltmeter in series.
- Place the resistor in the insulated container.
- Record the initial temperature of the resistor using the thermometer.
- Set the power supply to a low voltage.
- Record the voltage and current flowing through the resistor.
- Allow the circuit to run for a set time (e.g., 2 minutes).
- Record the final temperature of the resistor.
- Repeat steps 4-7 for several different voltage/current combinations.
Measuring Heat Produced:
The heat produced can be calculated using the following formula: Q = mcΔT, where Q is the heat energy (in Joules), m is the mass of the resistor, c is the specific heat capacity of the resistor material, and ΔT is the change in temperature (final temperature - initial temperature).
Expected Observations and Explanation:
You would expect to observe that as the current through the resistor increases, the temperature of the resistor also increases. This is because a higher current means more electrical energy is being converted into heat energy through Joule heating. The relationship between the heat produced and the current will be roughly proportional. The specific heat capacity of the resistor material will also influence the rate of temperature change. The insulated container helps to minimise heat loss to the surroundings, ensuring that the measured heat is primarily due to the resistor's internal heating.