✔ 最佳答案
1. For the pulsed square-wave form,
mean square current = (1/T).integral { (2I)^2.dt} with limit of t from 0 to T/2
= (4I^2/T).(T/2) = 2I^2
Hence, rms current = [square-root(2)].I = (1.414)I
For the sinusoidal dc wave form, the current i against time t can be represented by the eqiation:
i = I.sin(wt) + I
where w is the angular frequency, which equals to 2.pi/T
That is, it is a normal sinusoidal wave plus a constant dc curren I
SInce the rms current of I.sin(wt) is I/square-root(2), or (0.707)I, whereas the rms current of a constan current (a dc) is I.
The rms current of the sinusoidal dc
= square-root[(0.707I)^2 + I^2] = (1.225)I
2. I presume that the charge on the left-hand side of X is +Q and the one on the right-hand side of X is -Q
Consider the electric field at X, the electric field directions at X due to the two charges are the same, hence their field strengths add together,
a = kQ/r^2 + kQ/r^2
where k is the electrostatic constant (= 9x10^9 N.m^2/C^2)
i.e. a = 2kQ/r^2
thus, kQ/r^2 = a/2
Consider the point Y, the electric field directions due to +Q and -Q are in opposite directions, hence the field strength at Y, E, is given by
E = kQ/r^2 - kQ/(3r)^2
i.e. E = (8/9)(kQ/r^2) = (8/9).(a/2) =4a/9
3. When the Live wire is earthed accidentally, a short circuit occurs. There is no current flows through the other heater. The current, which flows directly from the 220v supply to earth, would be extremely large. This definitely blows the fuse.
2012-06-10 22:15:05 補充：
r.m.s. value of a quantity is the square root of the mean (average) of the square of that quantities. The mathematical equation is given in the web-page below:
http://en.wikipedia.org/wiki/Root_mean_square
