An analogue voltmeter has a resistance that is much less than that of a modern digital voltmeter - AQA - A-Level Physics - Question 3 - 2021 - Paper 3

The mirror on the voltmeter is used to eliminate parallax error when taking a reading. By reflecting the needle's position, it allows the observer to align their line of sight directly with the needle, minimizing visual distortion. This ensures that the measurement is as accurate as possible.

To calculate the percentage uncertainty in T₁₉, first find the mean time from the data provided in Table 1. The mean can be calculated as: T_{mean} = rac{12.00 + 11.94 + 12.04 + 12.16}{4} = 12.04 ext{ s} Next, take one reading, for instance, T₁₉ = 12.16 s. The uncertainty can be calculated using the formula: ext{Percentage Uncertainty} = rac{ ext{Uncertainty}}{ ext{Measurement}} imes 100 Assuming an uncertainty of ±0.1 s for manual readings, the calculation becomes: ext{Percentage Uncertainty} = rac{0.1}{12.04} imes 100 ext{ %} \\ ext{Percentage Uncertainty} ext{ = } 0.83 ext{ %}

The time constant τ for an RC circuit is given by the equation: $τ = R imes C$ By observing the discharge curve, we can determine that the time it takes for the voltage to drop to approximately 37% of its initial value is equal to the time constant. Given the values from the experiment, calculations would show this is approximately 17 s.

The student should ensure that the voltage across the capacitor does not exceed 3 V before connecting it to the 0 V and 3 V sockets. This can be accomplished by measuring the voltage across the capacitor with the voltmeter and ensuring it is within that range.

To develop the procedure for obtaining an accurate time constant, the student should:

1. Ensure the voltmeter is calibrated correctly before each measurement.
2. Record multiple measurements for each voltage drop and calculate a mean to reduce random error.
3. Use a consistent method for timing to ensure that each reading is taken at the same percentage voltage drop to obtain reliable comparisons.

From Figure 8, we linearize the relationship by plotting ln(V'/V) against time t. The slope of the line gives us -1/(RC) from which R can be calculated. Given the data points from the graph, the slope of the line corresponds to -1/16 kΩ. Thus, the calculated resistance of the voltmeter is about 16 kΩ.

The current I in the voltmeter can be determined using Ohm's law: I = rac{V}{R} Where V is the voltage at t = 10 s obtained from the data collected. If V is say 5 V and R is found to be 16 kΩ, then: I = rac{5V}{16 imes 10^3 ext{ Ω}} = 0.0003125 ext{ A} = 312.5 ext{ μA}