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A technician sets up a circuit as shown, using a car battery and two identical lamps - Scottish Highers Physics - Question 12 - 2016
Question 12
A technician sets up a circuit as shown, using a car battery and two identical lamps. The battery has an e.m.f. of 12.8 V and an internal resistance of 0-10 Ω. (a) ... show full transcript
Worked Solution & Example Answer:A technician sets up a circuit as shown, using a car battery and two identical lamps - Scottish Highers Physics - Question 12 - 2016
Step 1
Determine the reading on the voltmeter.
Answer
To find the voltmeter reading, we start with Ohm's law, where voltage V is given by:
Where:
- I is the current (1.80 A)
- R is the total resistance in the circuit.
The total resistance (R) includes the internal resistance of the battery (0.10 Ω) and the resistance of the two lamps in series (4.8 Ω each):
Now, substituting the values: gives
However, the emf of the battery is 12.8 V. Thus, using Kirchhoff’s voltage law, the voltmeter reading can be found as:
ightarrow V = 4.0 V $$Step 2
State the effect this has on the reading on the voltmeter.
Answer
When switch S is closed, the total current in the circuit increases as the lamps are connected in parallel, thereby decreasing the total resistance of the circuit. Consequently, this results in:
- An increase in the current passing through the circuit.
- A decrease in the voltage across the voltmeter as the voltage drop across the lamps will now be derived from a lower total resistance.
Thus, the reading on the voltmeter would decrease.
Step 3
Using band theory, explain how the LED emits light.
Answer
In a forward-biased LED, electrons from the p-type material are injected into the n-type material. When voltage is applied across the LED, electrons move towards the conduction band, overcoming the band gap, and drop to the valence band. By this process, energy is released in the form of photons:
- The movement of electrons from the conduction band to the valence band results in a decrease in energy levels and the emission of light.
Thus, the energy difference reflected in the emitted light corresponds to the band gap of the LED.
Step 4
Calculate the wavelength of the light emitted by the LED.
Answer
Using the energy-wavelength relation: E = rac{hc}{ ext{wavelength}} where:
- h = Planck's constant
- c = speed of light Given that the band gap for the LED is: Substituting into the formula:
ext{wavelength} = rac{hc}{E}
Substituting known values:
- h = 6.63 × 10⁻³⁴ J·s
- c = 3 × 10⁸ m/s,
Calculating gives:
ightarrow ext{wavelength} ext{ in meters} = 6.56 imes 10^{-7} ext{ m} $$.Step 5