physics PLZ HELP

1 When two lamps are connected in series to a battery, the brighter lamp has a bigger resistance than the less bright lamp
WHY INCORRECT ?
When lamps are connected in series, the current(I) flowing should be the same through these lamps. As a brighter lamp has more power consumed, by P=I2R, the brighter lamp should have a higher resistance. So this statement must be correct. Perhaps you would have a double check on where this statement was quoted?

2 If the power loss of the transmission cable is calculated by I2R,
what is the voltage across the cable?
Let P(in) be the power input
　 P(cable) be the power transmitted across the cable
　 P(loss) be the power loss against the resistance in the cable

P(in) = P(cable)+P(loss) = V(cable) x I + I2R
V(cable) = [P(in) - I2R] / I
To find the voltage transmitted across the cable, the power input must be known. Otherwise, the information is insufficient to find the useful output power.

3 When the neutral wire touches the metal case, will there be current flowing through the earth wire if the switch is on?
In a neutral wire, the voltage is zero since it is earthed. If it accidentally touches the metal case connected to the earth wire, whether there is current flow through it should we consider the resistance among the metal case and the neutral wire, due to the 0V voltage of both. Since a currect tends to flow through a path without resistance, if the resistance in the neutral wire is zero, then there must be no current flowing through the metal case; but practically, there is somehow resistance in the neutral wire, so the current will be distributed between the wire and the case with a higher magnitude in the lower resistance one.

(Due to the letter limit, I will type more in the supplymentary column.)

2010-04-11 12:56:05 補充：
4 What is BACK E.M.F.?
The induced back emf in a coil is directly proportional to the rate of change of magnetic flux linkage through the coil.

2010-04-11 13:00:57 補充：
5

2010-04-11 13:01:40 補充：
The transformer equation is only suitable for an ideal transformer

2010-04-11 13:03:52 補充：
6

2010-04-11 13:05:49 補充：
The figure limit is too strict. Feel free to PM me if you have questions.

1 when two lamps are connected in series to a battery, the brighter lamp has a bigger resistance than the less bright lamp
WHY THIS STATEMENT IS INCORRECT ?
this statement is correct because power = current x current x resistance, therefore the higher the resistance the higher the power.

2 the power loss of the of the transmission cable is calculated by I2R
what is the voltage across the cable
using ohm's law, voltage = current x resistance

3 when the nuetral wire touches the metal case will there be current flowing through the earth wire if switch is on
yes, current flows through the metal case and earth wire may cause electric shock.

4 what is BACK E.M.F.
back emf is a self-induced emf when the magnetic field of a solenoid collapses and cut through the coil conductor.