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Alternating currents Cambridge International AS & A Level Physics revision

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In plain words

The mains doesn't push current steadily one way, as a battery does. It pushes it back and forth, fifty times a second, in a smooth wave. Because the value keeps changing we need a sensible kind of average to describe it, and that is the r.m.s. value: the steady current that would give the same heating.

4 things to know

  1. A sinusoidal alternating current or p.d. is described by x = x₀ sin ωt, where x₀ is the peak value and ω = 2πf. The period is T = 1 ÷ f.
  2. The root-mean-square (r.m.s.) value is the steady value that would dissipate the same power in a resistor. For a sine wave, r.m.s. current = I₀ ÷ √2 and r.m.s. p.d. = V₀ ÷ √2.
  3. The mean power in a resistor is half the maximum power: mean P = ½I₀²R, which is the same as (r.m.s. current)² × R.
  4. Mains voltages are quoted as r.m.s. values. A 230 V supply has a peak of 230 × √2 = 325 V.

Worked example

An alternating p.d. with a peak value of 12 V is connected across a 6.0 Ω resistor. Find the r.m.s. p.d. and the mean power.

  1. R.m.s. p.d. = 12 ÷ √2 = 8.5 V.
  2. Mean power = (r.m.s. p.d.)² ÷ R = 72 ÷ 6.0.
  3. = 12 W, which is half the maximum power of 12² ÷ 6.0 = 24 W.

Tips and tricks

  • Use r.m.s. values to find mean power, and peak values to find maximum power.
  • In V = V₀ sin ωt, the number in front of t is ω. Divide it by 2π to get the frequency.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Alternating currents: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. An alternating p.d. has a peak value of 10 V. What is its r.m.s. value?
    • 5.0 V
    • 7.1 V (the answer)
    • 10 V
    • 14 V

    10 ÷ √2.

  2. For a sinusoidal current in a resistor, how does the mean power compare with the maximum power?
    • It is half. (the answer)
    • It is the same.
    • It is a quarter.
    • It is 0.71 times.

    The mean of sin² over a cycle is a half.

  3. An alternating supply has a frequency of 50 Hz. What is its period?
    • 0.0020 s
    • 0.020 s (the answer)
    • 0.50 s
    • 50 s

    T = 1 ÷ f.

  4. What does the r.m.s. value of an alternating current tell you?
    • the steady current that would give the same power in a resistor (the answer)
    • the greatest value of the current
    • the average of the current over a cycle
    • the current at the start of each cycle

    The plain average over a full cycle would be zero.

  5. An alternating p.d. is given by V = 20 sin(314t). What is its peak value?
    • 20 V (the answer)
    • 14 V
    • 314 V
    • 50 V

    The number in front of the sine is the peak value.

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