Question

A power line running East-West at 150kVAC carrying a 75MWatt load is 10 meters overhead. A thief makes a 100 turn loop of insulated copper wire around a plastic garbage can with a 70cm diameter. The voltage generated in this coil is used to charge batteries for a fish-finder, lights and radio in his fish hut. The battery charger is electrically equivalent to a 5 ohm resistor.

a) [2] What orientation of the garbage pail winding will allow the greatest rate of electricity theft?

b) [4] Determine the voltage generated across the battery charger.

c) [2] Residential power costs $0.10/kWh. What is the value of the power stolen per day.

d) [2] Why would metal can be a bad choice?

e) [4] Above the indication is that the other wire for the AC power transmission is very far away. In fact they both hang from the same structure. If each wire carries a 100amp current and they are separated by 50cm, determine the force per unit length on the wires

Answer 1

(a) Orientation of coil of 100 turns with respect to overhead current carrying wire for getting maximum EMF is shown in figure. Axis of 100 turns coil should be perpendicular to the overhead wire in order to get maximum induced EMF.

If power line is running in the direction of East-West, then 100 turns coil axis should be in North-South direction

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(b) induced EMF E in the coil is given by,

......................(1)

where is flux of magnetic field, N is number of turns, B is flux density of magnetic field, and A is area of cross section of coil.

Flux density of magnetic field B is given as

.............................(2)

where I is current passing through wire and d is distance between wire and centre of 100 turns coil

RMS value of AC current I = Power Load / Voltage = ( 75 10⁶ ) / ( 150 10³ ) = 500 A

AC current is considered as, I = 500 sin(t ) ....................(3)

where = 260 = 120 rad/s is angular frequency. (It is assumed AC current frequency 60 Hz )

From eqn.(1) and (2) we get

RMS value of induced EMF is given by

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(c) Power P drawn from induced EMF is given by,

Energy consumed in a day in terms of kW-h = 4.205 10^-6 24 = 10^-4 kW-h

cost of energy consumption = 10^-4 0.1 = $10^-5

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(d) If metal is used instead of plastic container , eddy current induced in metal will give induced emf which is in opposite direction of induced emf in coil . Hence induced emf in coil will be reduced

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(e) force between current carrying wires per unit length is given by