Yusong

Yusong 25 Aug 2016

Question

The figure shows a long horizontal wire PQ carrying a steady current of 50A in the direction QP. A copper wire RS of diameter 0.40mm hangs horizontally at a distance of 0.15m below wire PQ using some threads.

A current flows through RS such that there is no tension in the threads.

Identify the direction is the current and draw a free body diagram of the forces acting on RS.

Answer

If the current in RS is flowing opposite to the current in PQ, the two wires will repel each other.

Since the wire is suspended in equilibrium, the resultant force must be zero.

Fup = Fdown
T1 + T2 = FB + W

We can see that it is not possible for the tension to be zero.

 

If the current in RS is flowing in the same direction as the current in PQ, the two wires will repel attract other.

Since the wire is suspended, the resultant force must be zero.

Fup = Fdown
T1 + T2 + FB = W

When the tensions in both threads are zero, we have

FB = W

Hence, current in RS must be flowing in the same direction as PQ, in the direction SR.

The free body diagram when there is no tension in the threads is as shown below:

Yusong 04 Aug 2016

Question

A simple iron-core transformer is shown below:

Suggest why thermal energy is generated in the core when the transformer is in use.

Answer

Consider a section of the transformer core which is coloured blue as shown below:

As the magnetic field produced by the current in the primary coil increases, the magnetic flux linkage of the section of the coil will increase.

By Faraday’s Law, there will be an induced e.m.f. produced in the section of the core. By Lenz’s Law, there will be a current flowing in the section of the core which will produce a magnetic effect to oppose the change.

By the Right Hand Grip Rule, this means that a circular current must be flowing in the section of the core in order to produce the magnetic field. (This circular current is called the eddy current.)

Since an induced current is flowing in the core, by P = I 2 R, there will be power dissipated in the core and thermal energy is generated in the core of the transfomer.