A student was investigating capacitors and set up the circuit shown. The student planned to use the circuit to measure the potential difference V across the capacitor C as it was charged and discharged through the resistor R. (a) Give two reasons why the circuit did not operate as intended. (b) The student moved the switch from position X to position Y at time t = 0 s. The student recorded values of V as t increased and plotted the graph shown. The capacitance of capacitor C was 2.2 µF. (i) Determine the resistance in the circuit when the switch was at position Y. (ii) Determine the average current in the circuit between t = 0 s and t = 30 s. (iii) Calculate the energy dissipated by the current in the circuit between t = 0 s and t = 30 s.

A-Level Edexcel Physics Capacitance: A student was investigating capa

A student was investigating capacitors and set up the circuit shown - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 4

Question 16

A student was investigating capacitors and set up the circuit shown. The student planned to use the circuit to measure the potential difference V across the capacit... show full transcript

Worked Solution & Example Answer:A student was investigating capacitors and set up the circuit shown - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 4

Step 1

Give two reasons why the circuit did not operate as intended.

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Answer

Switch Position: If the switch was not connected properly to position Y, the circuit wouldn't close correctly, preventing current from flowing.
Capacitor Failure: If the capacitor C is faulty or has not been charged initially, it will not store the charge needed to measure the potential difference.

Step 2

Determine the resistance in the circuit when the switch was at position Y.

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Answer

To determine the resistance, we can use the time constant formula for a capacitor in an RC circuit. The voltage across the capacitor (V) can be expressed as:

$V(t) = V_0 (1 - e^{-t/RC})$

Given that the capacitance C = 2.2 , ext{µF} = 2.2 \times 10^{-6} , ext{F}, we can rearrange the formula to find R using the values from the graph.

Step 3

Determine the average current in the circuit between t = 0 s and t = 30 s.

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Answer

The average current can be calculated using the formula:

$I_{avg} = \frac{Q}{\Delta t}$

where Q is the charge and can be calculated using the capacitance and the voltage at t = 30s, and \Delta t = 30 s.

Step 4

Calculate the energy dissipated by the current in the circuit between t = 0 s and t = 30 s.

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Answer

The energy (E) dissipated in the circuit can be calculated using the formula:

$E = I^2 R t$

where I is the average current calculated previously, R is the resistance, and t is the time interval from 0 s to 30 s.

A student was investigating capacitors and set up the circuit shown - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 4

Worked Solution & Example Answer:A student was investigating capacitors and set up the circuit shown - Edexcel - A-Level Physics - Question 16 - 2023 - Paper 4

Give two reasons why the circuit did not operate as intended.

Determine the resistance in the circuit when the switch was at position Y.

Determine the average current in the circuit between t = 0 s and t = 30 s.

Calculate the energy dissipated by the current in the circuit between t = 0 s and t = 30 s.

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