How is the efficiency of transformers improved by better design?
A typical set up...
Resistance Power cable resistivity is very low but because of the long distances involved, it begins to make a difference. The resistance from the local PowerStation to the school would be roughly 100 Ω. Voltage lost = current x resistance (V = IR) Without the transformer V = 4000 x 100 V = 400000V With the step up transformer V = 250 x 100 V = 25000V Voltage dropped as heat
Step Down Transformers
There are transformers along the grid that slowly step down the voltage, this is because heavy industry, light industries and homes need a different voltage.
25 KV 275KV 132KV 11kV 5KV 230V 230V
How does a transformer work? There is a primary and secondary coil What is the relationship between the ratio of the number coils and the ratio of the voltages between the primary and secondary coil? 3V ac Bulb 1 2 iron cores pushed together Warning : form a powerful electromagnet Bulb 2 Primary Coil Secondary Coil Primary coil Secondary coil 10 turns 20 turns 20 turns 10 turns 15 turns 30 turns 30 turns 15 turns Bulb 1 Bulb 2
The Transformer Rule
Transformers consist of two coils, a primary and secondary coil. When an AC current is connected to the primary coil it produces a magnetic field in the iron core
The field cuts the secondary coil and induces an alternating current Magnetic flux (Greek letter Φ (phi)), is a measure of the magnetic field strength. The transformer is designed so that all the magnetic flux from the primary coil is transferred to the secondary coil Flux linkage is a property of a coil of conducting wire and the magnetic field through which it passes. It is determined by the number of turns of the coil (N) and the flux (Φ) of the magnetic field. The Flux linkage in the secondary coil = N s Φ N S is the number of turns in the secondary coil The Induced emf in the secondary coil is equal to the rate of change of the magnetic field. The stronger the field or the quicker the change in magnetic field the greater voltage induced will be. V s = N s d Φ dt
= N p d Φ dt Similarly the voltage induced in the primary coil can be derived the same way The applied voltage Vp opposes the induced voltage, assuming the coils have zero resistance, the applied voltage equals the induced voltage V p = N p d Φ dt Dividing equation for Vs by the equation for Vp N p d Φ dt V s = N s V p N p This is the transformer rule Step up has more turns on the secondary coil. The voltage goes up and the current goes down Step down has more turns on the primary coil. The voltage goes down but the current goes up V s = N s d Φ dt V p
To make transformers as near as 100% efficient they have …
Low resistance windings to reduce heating A laminated core consisting of iron separated by insulators to reduce eddy currents in the metal core A core of soft iron which is easily magnetised. Efficiency = Power delivered by the secondary coil Power supplied to the primary coil
1. The needle kicks in one direction (say to the right) because as the current rises in circuit 1, there is a change in magnetic flux. Some of this flux is linked with circuit 2, inducing a current in this complete circuit.
No deflection as the flux is not changing when the current is constant.
The needle kicks in the opposite direction to question 1 as there is a flux change in the opposite direction, i.e. flux is collapsing instead of growing.
The meter shows a steady deflection in ac mode.
The flux linkage between the coils is constantly changing due to the constantly changing current.
Circuit B is more economical. In circuit B, current flows through the transformer only when the bell push is pressed. In circuit A, current flows through the primary circuit at all times, which wastes energy.
7. A large flux is linked due to the presence of the iron core and a very large number of turns on the secondary winding. The contact is broken quickly, causing a large change of flux in a short time. According to Faraday’s law, this produces a very high voltage for a short time.
8 (a) Vs / Vp =Ns / Np , so Ns = (Np x Vs) / Vp. So (3000 X 9 V) / 230 V = 117.4 » 117 turns (nearest whole no.) (b) Any two of the following: Incomplete flux linkage between coils Resistance of primary coil Eddy currents induced in core (c) With steady dc input the magnetic flux is constant so no emf will be induced in the secondary coil