Simulation
The operation of the circuit can be simulated as shown below. During 0 <
q < p , the expression
for current is:
i(q) = A * exp [ -(q - a)/t)
+ (E/Z)*sin (q - b ),
where t = wL/R, b =
atan (t), Z2 = R2 + (wL)2
= R2*(1 + t2 and a
is the firing angle.
During p < q <
(2p + a), the expression for current is:
i(q) = A*exp {- (q - a) /t}
+ (E/Z)*sin (p - b)*exp
{- (q - p) /t} .
The voltage across the inductor is obtained to be
vL(q ) = vs(q)
- R*i(q) , for a <
q < p and
vL(q ) = - R*i(q)
, for p < q <
(2p + a) .
vs(q) = E*sin (q).
It is preferable to normalize vs with respect to E and the current
with respect to E/R and then the only value that is required to be known for
solving for the current is t. The applet shown
below simulates this circuit. You have to key-in the ratio t
in the text-field to the left of the button and the firing angle in degrees
in the text-field to the right of the button and then click on the button
next to it. Do not key-in
a NaN.
click here to open the applet
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