A permanent magnet is attached to a vertical spring so that it undergoes simple harmonic motion. A coil of conducting wire is arranged so that when the magnet is displaced vertically it oscillates in and out of the coil, inducing a sinusoidal alternating current (ac) of rms value 1.65 mA.
(a)
(i)
Explain in words how the rms value of the alternating current relates to a direct current of 1.65 mA.
[1]
(ii)
Sketch the graph shape which would be expected from this direct current.
[1]
(iii)
Sketch the graph shape which would be expected from this ac current.
A different transformer is used to transmit power to a village.
The transmission cables connecting the power station to the transformer have a total resistance of 3.5 Ω. The transformer is 92% efficient and steps down the voltage to 220 V. At the time of maximum power demand the effective combined resistance of the cables to the village and the village is 50 mΩ.
(c)
Calculate the current in the cables connected to the village.
Electrical power is produced for the national electricity grid using a series of alternating current (ac) generators connected to identical transformers.
The following data are available for one transformer. All values are root mean squares (rms).
ac generator output voltage to a transformer
= 35 kV
ac generator output current to a transformer
= 2.8 kA
Transformer output voltage to the grid
= 330 kV
Transformer efficiency
= 96%
(a)
Calculate the current output by this transformer to the grid.
A transformer has 700 turns in its primary coil and 300 in the secondary coil. An ac voltage of 220 V and frequency 50 Hz is established in the primary coil.
