A-level Physics (Advancing Physics)/Transformers/Worked Solutions

'''1. A step-down transformer has 300 coils on one coil, and 50 coils on the other. If 30 kV AC is put in, what voltage comes out?'''

$$\frac{300}{50} = \frac{30000}{V_s} = 6$$

$$V_s = \frac{30000}{6} = 5\mbox{ kV}$$

'''2. A step-up transformer has 200 coils on one coil, and 980 coils on the other. If 25 kV AC comes out, what voltage was put in?'''

$$\frac{200}{980} = \frac{V_p}{25000}$$

$$V_p = \frac{25000 \times 200}{980} \approx 5.1\mbox{ kV}$$

'''3. An ideal transformer transforms a 50A current into a 1A current. It has 40 coils on the primary coil. How many coils are in the secondary coil?'''

$$\frac{50}{1} = \frac{N_s}{40} = 50$$

$$N_s = 40 \times 50 = 2000\mbox{ coils}$$

'''4. Transformers tend to vibrate. Why is this? What effect does this have on the efficiency of the transformer?'''

There are wires with current in them going perpendicularly through a magnetic field. According to F = BIL, a force is exerted on the wires. This means that some of the energy is converted into kinetic energy, reducing the efficiency of the transformer.

'''5. Air does have some permeability. What effect does this have on the efficiency of the transformer? Why?'''

Some of the flux passes through the air instead of the core, and so does not pass through the secondary coil, and is not used to create AC. This means that some of the energy put in oscillates in and out of the magnetic field, reducing the efficiency of the transformer.