Electromagnetism Notes-3 Electromagnetic Induction The Transformer and its use in the National Grid

Model National Grid-1

Model National Grid-1 Voltage IN /V Power of bulb /W Voltage OUT /V 2.5 0.75 0.9

Model National Grid-1 Voltage IN /V Power of bulb /W Voltage OUT /V 2.5 0.75 0.9 Voltage IN /V Power of bulb /W Voltage OUT /V 12 24 1.4

Model National Grid-2

Model National Grid-2 Voltage IN /V Power/W Turns ratio Step-up V OUT /V Step-down V IN /V Final Voltage OUT /V 2.5 0.75 1 : 10 22 18 10 : 1 1.7

Model National Grid-2 Voltage IN /V Power/W Turns ratio Step-up V OUT /V Step-down V IN /V Final Voltage OUT /V 2.5 0.75 1 : 10 22 18 10 : 1 1.7 Voltage IN /V Power/W Turns ratio Step-up V OUT /V Step-down V IN /V Final Voltage OUT /V 12 24 1 : 20 220 180 20 : 1 9.1

Inducing an emf without physical movement

Inducing an emf without physical movement-2

Magnetic circuit links electric circuits

Inducing an emf without physical movement-3

Faraday’s transformer 1831

Transformer principle-1

Transformer principle-2 Primary Turns Secondary Turns Input Voltage /V Output Voltage /V 30 10 2.16 0.71 20 1.45 2.18 40 2.93 50 3.50 60 4.38

Questions Independent variable ? Kind of variable ? Control variables ? How does output voltage depend on Number of turns ? Type of input voltage ?

Graph of Output Voltage /V against No. of turns From graph, how does output voltage depend number of turns on secondary coil ?

The Transformer Equation

Energy Losses in a transformer In practice, if the voltage is doubled the current is more than halved due to small energy losses in the transformer:- The windings of copper wire do have resistance and heat is produced in them The alternating magnetic flux induces currents in the core, Eddy currents, which cause heating in the iron core The field lines in the core are repeatedly changed from one direction to the other and back again. This requires energy and also causes the core to get hot. Leakage of field lines in the iron core reduces the output voltage and current

Step down transformer

Alternative National Grid model

Low voltage transmission

Efficiency of low voltage transmission Voltage IN = 11.9 V Voltage OUT = 1.4 V Current IN = 2.79 A Current OUT = 0.68 A Power IN = 11.9 x 2.79 Power OUT = 1.4 x 0.68 = 15.6 W = 1.1 W Efficiency = Power IN / Power OUT Efficiency = 1.1 / 15.6 = 7%

High voltage transmission

Efficiency of high voltage transmission Voltage IN = 12.5 V Voltage OUT = 10.0 V Current IN = 2.32 A Current OUT = 1.60 A Power IN = 12.5 x 2.32 Power OUT = 10.0 x 1.60 = 29.0 W = 16.0 W Efficiency = Power IN / Power OUT Efficiency = 16 / 29 = 55%

Currents in an ideal transformer For a transformer, with no energy losses, i.e. 100% efficient Power IN = Power OUT If the output voltage is doubled, the output current is halved. A small current at high voltage delivers same power as large current at low voltage. A power of 1000W can be delivered by Current of 10A at voltage 100V or Current of 1A at 1000V

Heating effect of a current Much Greater heating effect with large current than with small current. Power (W) = (Current in A)2 x Resistance (Ω) 10 fold increase in voltage leads to 10 fold decrease in current and a 100 times decrease in heat produced