Alternating currentsAQA A-Level Physics: Subtopic test

1. 1
   A heating element of resistance 46 Ω is connected to the UK mains supply, which has an rms voltage of 230 V and a frequency of 50 Hz. The supply voltage is sinusoidal.

   (a)

   What is the peak voltage of the supply?

   [1 mark]

   • A163 V
   • B230 V
   • C325 V
   • D460 V

   (b)

   What is the mean power dissipated in the heating element?

   [1 mark]

   • A5.0 W
   • B1150 W
   • C2300 W
   • D4600 W

   (c)

   Explain why the mean power dissipated in the element is half of its maximum instantaneous power.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   An oscilloscope is used to display a sinusoidal alternating voltage. The Y-gain is set to 2.0 V per division and the time-base to 5.0 ms per division. The trace has a peak-to-peak height of 5.2 divisions, and one complete cycle of the trace occupies 4.0 divisions horizontally.

   (a)

   What is the peak voltage of the signal?

   [1 mark]

   • A5.2 V
   • B10.4 V
   • C3.7 V
   • D2.6 V

   (b)

   What is the frequency of the signal?

   [1 mark]

   • A20 Hz
   • B200 Hz
   • C0.05 Hz
   • D50 Hz

   (c)

   Calculate the rms voltage of the signal.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A signal generator supplies a sinusoidal alternating current of peak value 1.5 A and frequency 400 Hz to a resistor of resistance 12 Ω.

   (a)

   Calculate the rms current and the mean power dissipated in the resistor.

   [3 marks]

   (b)

   Calculate the peak-to-peak voltage across the resistor, and the current 0.50 ms after the current passes through zero while increasing, using I = I₀ sin 2πft.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A 20 Ω heating element is connected first to a 12.0 V direct current supply and then to a sinusoidal alternating supply. The student wants the alternating supply to heat the element at the same mean rate as the direct supply, and uses an oscilloscope to check the output of the alternating supply.

   (a)

   Explain what is meant by the rms value of an alternating voltage, why the mean value of the voltage cannot be used to compare the heating effects, and what rms value the alternating supply should have.

   [6 marks]

   (b)

   The oscilloscope shows a trace with a peak-to-peak height of 6.8 divisions at a Y-gain of 5.0 V per division. Calculate the rms voltage, and the mean power in the element for the alternating and the direct supplies. Justify whether the student has set the alternating supply correctly.

   [6 marks]

   Total for question 4: 12 marks

End of questions