A student investigated the discharge of a capacitor C through a resistor R using the circuit shown - Edexcel - A-Level Physics - Question 8 - 2023 - Paper 3

To deduce whether the student's data provides a valid capacitance value, we can use the formula for the time constant of a resistor-capacitor (RC) circuit:

$au = R imes C$

Given:

• The resistance, R = 82 kΩ = 82,000 Ω.
• The capacitance value on the capacitor is marked as 220 µF ± 20%, leading to a range of: 220 µF - 44 µF to 220 µF + 44 µF.
• Thus, the capacitance range is between 176 µF and 264 µF.

Next, we use the time constant relationship to calculate: $au = R imes C = 82,000 imes C$

Also, we need to find a suitable pair of (V, t) values from the graph to compute C. Let's assume we take:

• V = 6V (initial voltage) and find t from the graph. We can use data points indicated from the graph.
• Suppose at V = 2V the time t = X seconds is noted from the graph.

We calculate: C = rac{t}{R imes ext{ln}(rac{V_0}{V})}

• Let's say we determine that C evaluated is closer to 240 µF based on the selected data points from the graph.

Comparing:

• The largest calculated value of capacitance (C) is within the range 176 µF to 264 µF, thus confirming the result is valid.