00:02
The impedance of the circle is given by equation 30 -28b, and we divide the magnitude of the ac voltage by the impedance to get the magnitude of the ac current in the circuit.
00:14
So z is equal to the square root of r squared plus wl minus 1 over wc squared.
00:25
And that equals wl minus 1 divided by wc, i .0 is equal to v20 over z, which is equal to v20 over wl minus 1 over wc.
00:46
So i of t is equal to v20 over wl minus 1 over wc, sine of w t minus pi over 2.
01:04
For b, we treat the emf as a superposition of the ac and dc components.
01:18
And so we start with vl is equal to l, di over dt, and that's equivalent to l, d over dt, which is v20 over wl minus 1 over wc, sign of wt minus pi over 2.
01:44
Which equals v20 l w over wl minus 1 over wc, cosine wt minus pi over 2, which lastly equals v20lw over wl minus 1 over wc, sine of wt...