Alternating Current & Voltage

Curriculum Level

This lesson is designed for AQA A-Level Physics (Year 13) and aligns with the UK A-Level specification, specifically the "Further Mechanics and Thermal Physics" section, under the topic of "Alternating Currents."

Lesson Objectives

By the end of this 60-minute lesson, students should:

• Understand the fundamental principles of alternating current (AC) and alternating voltage
• Describe and calculate root mean square (rms) values
• Apply knowledge to resistive, capacitive, and inductive AC circuits
• Solve AQA-style exam questions with detailed reasoning

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Lesson Structure (60 Minutes)

1. Starter Activity – 5 Minutes

Engagement Question:
Display two waveforms on the board – one a DC signal and one an AC signal. Ask:
👉 Why do we use alternating current in household electricity instead of direct current?
Encourage students to discuss in pairs for 2 minutes before taking brief responses.

🛠️ Teacher’s Explanation:

• DC provides a constant voltage in one direction
• AC continuously changes direction, making it more efficient for power transmission
• The UK mains electricity operates at 230V rms and 50 Hz

2. Core Theory – 15 Minutes

Understanding Alternating Current and Voltage

Use a sine wave diagram to introduce key AC concepts:

• Peak Voltage (V₀) – Maximum value of voltage
• Instantaneous Voltage (V) – Varies with time, given by:
  [ V = V_0 \sin(\omega t)
  ]
  where ω is the angular frequency (ω = 2πf)

Root Mean Square (rms) Voltage

• The rms value of an alternating voltage is the equivalent DC voltage that produces the same power.
• Given by:
  [ V_{\text{rms}} = \frac{V_0}{\sqrt{2}}
  ]
  Similarly,
  [ I_{\text{rms}} = \frac{I_0}{\sqrt{2}}
  ]

Power in an AC Circuit

• Just like in DC circuits, power is given by:
  [ P = IV
  ]
  but using rms values:
  [ P = V_{\text{rms}} I_{\text{rms}}
  ]
• In purely resistive loads, P = I²R or P = V² / R

🎯 Quick Discussion:
📌 Why don’t we use peak values when calculating power?

3. Worked Example – 10 Minutes

Problem: A UK mains socket provides 230V rms at 50 Hz. Calculate:

1. The peak voltage (V₀)
2. The period (T) of the waveform

✍ Solution:
Using:
[ V_0 = V_{\text{rms}} \times \sqrt{2}
]
[ V_0 = 230 \times 1.414
]
[ V_0 ≈ 325V
]

For period:
[ T = \frac{1}{f} = \frac{1}{50}
]
[ T = 0.02s \quad \text{(or 20ms)}
]

4. Application to Exam Questions – 15 Minutes

Students now attempt the following AQA exam-style questions individually:

Question 1

A coil in an AC circuit has an alternating voltage given by:
[ V = 240\sin(314t)
]
(a) Determine the peak voltage of the supply.
(b) State the frequency of the supply.
(c) Calculate the rms voltage.

✏️ Answers:
(a) Peak Voltage = 240V (the coefficient of sine)
(b) Given ω = 314 rad/s, use ω = 2πf to solve for f:
[ f = \frac{314}{2\pi} = 50 Hz
]
(c)
[ V_{\text{rms}} = \frac{V_0}{\sqrt{2}} = \frac{240}{1.414} ≈ 170V
]

Question 2 (Exam Challenge)

A resistor of 10Ω is connected to a 230V rms AC supply. Calculate:
(i) The rms current through the resistor.
(ii) The average power dissipated in the resistor.

✏️ Solutions:
(i) Using Ohm’s Law (V = IR):
[ I_{\text{rms}} = \frac{V_{\text{rms}}}{R} = \frac{230}{10} = 23A
]
(ii) Power formula:
[ P = V_{\text{rms}} \times I_{\text{rms}} = 230 \times 23 = 5290W
]

5. Plenary – 10 Minutes

🗣️ Discussion Questions:

1. What would happen if household electricity was supplied as DC instead of AC?
2. Why don't we feel the rapid voltage oscillations of the 50Hz mains supply?
3. Airlines use 400Hz AC instead of 50Hz – why do you think this is useful?

🏆 Exit Quiz (Whiteboard or verbal recap)

• Define rms voltage
• Write down the equation for instantaneous voltage
• A mains socket is 230V rms – what is the peak voltage?

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Extension Activities (for early finishers)

• Research how a transformer works and write down where rms values come into play
• Explore why AC transmission is more efficient than DC

Assessment & Homework

• Students complete past AQA AC circuit exam questions for homework
• Marking will assess fluency in calculations, conceptual understanding, and reasoning

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Teacher Notes:

• Ensure students understand why rms values are used
• Use oscilloscopes or simulations (if available) to visually demonstrate AC behavior
• Relate AC principles to real-world applications (e.g., why phone chargers use transformers)

(This lesson follows specific UK AQA A-Level Physics curriculum requirements and challenges students to apply mathematical reasoning to AC concepts.) 🚀