ELECTRICITY & ELECTROMAGNETISM

1. Current flows through the upper resistors branch (i.e. the 3-ohm and 6-ohm in series) = 9/(3+6) A = 1 A

Current flows through the lower resistors branch (i.e. the 4-ohm and 2 ohm resistors in series) = 9/(2+4) A = 1.5 A

Taking the negative terminal of the battery as a zero potential reference, potential at junction between 3-ohm and 6-ohm resistors = 1 x 6 v = 6 v
Potential at junction between 4-ohm and 2 ohm resistors = 1.5 x 2 v = 3 v
Hence, potential difference between the two junctions = (6-3) v = 3 v

Therefore, a reading of 3 v should be recorded by an ideal voltmeter.

Since the voltmeter is not ideal, there is a small current flowing through the voltmeter from the upper junction to the lower junction. The current through the 6-ohm resistor is slightly less than 1 A, hence the potential at the upper junction will be slightly less than 6 v.

Likewise, the current through the 2-ohm resistor is slightly larger than 1.5 A. The potential at the lower junction is thus slightly higer than 3 v.

Now, the potential of the upper junction is slightly lower than 6v, whereas that of the lower junction is slightly higher than 3v. The voltmeter reading will thus be slightly less than 3 volts.

[Note: the voltmeter measures the potential difference between the upper and lower junction]


2. Apply "Right Hand Screw Rule" to wire X at the position of compass I. The magentic field lines are in the direction from left to right. Thus the compass needle will be deflected clockwise.

When the Right Hand Screw Rule is applied to the "U region" of the wire, magnetic field lines are all pointing downward at position of compass II. Since the compass needle can only be rotated in a horizontal plane, there will not be any effect on the needle. Hence, it will remain in the same position as before.