The circuit shows a 1 mF capacitor connected to an a.c. supply. The graph shows how the potential difference V varies with time t. (a) (i) Calculate the root-mean-square potential difference. Root-mean-square potential difference = (ii) The formula used to generate this graph is V = 5 sin(100πt) Explain why this formula leads to the graph above.

A-Level Edexcel Physics Waves: The circuit shows a 1 mF capacit

The circuit shows a 1 mF capacitor connected to an a.c - Edexcel - A-Level Physics - Question 18 - 2023 - Paper 1

Question 18

The circuit shows a 1 mF capacitor connected to an a.c. supply. The graph shows how the potential difference V varies with time t. (a) (i) Calculate the root-mean-s... show full transcript

Worked Solution & Example Answer:The circuit shows a 1 mF capacitor connected to an a.c - Edexcel - A-Level Physics - Question 18 - 2023 - Paper 1

Step 1

Calculate the root-mean-square potential difference

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Answer

The root-mean-square (RMS) potential difference for an alternating current (AC) waveform can be calculated using the formula:

$V_{rms} = \frac{V_{max}}{\sqrt{2}}$

In this case, the maximum potential difference, $V_{max}$ , can be identified from the equation ( V = 5 \sin(100\pi t) ), where $V_{max} = 5V$ . Thus:

$V_{rms} = \frac{5}{\sqrt{2}} \approx 3.54 \text{ V}$

Step 2

Explain why this formula leads to the graph above

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Answer

The formula ( V = 5\sin(100\pi t) ) represents a sinusoidal waveform, which is characteristic of alternating current. The sine function oscillates between -5V and +5V, resulting in a repetitive smooth wave shape.

Amplitude: The amplitude of the wave (5V) indicates the maximum potential difference reached at peaks.
Frequency: The term ( 100\pi ) corresponds to the frequency of the wave, affecting how fast it completes one cycle. The period of the waveform can be derived from the angular frequency as:

$T = \frac{2\pi}{100\pi} = 0.02 \, s$

This explains the horizontal periodicity as observed in the graph. Each cycle of this wave corresponds to a rise and fall in the potential difference, which is depicted in the provided graph.

The circuit shows a 1 mF capacitor connected to an a.c - Edexcel - A-Level Physics - Question 18 - 2023 - Paper 1

Worked Solution & Example Answer:The circuit shows a 1 mF capacitor connected to an a.c - Edexcel - A-Level Physics - Question 18 - 2023 - Paper 1

Calculate the root-mean-square potential difference

Explain why this formula leads to the graph above

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