Hello everyone on the problem bellow i have come up with a possible solution thats needs evaluation, thanks for helping
What we need to find is the value of Zx that will make Vo=0
So first i took the ideal transformer equations and had V2/v1 = a ( assuming that v2 and v1 are the voltages on the secondary and primary respectively
we also have i2/i1 = 1/a => i1=a*i2 or in mesh currents we have I1I3=a*(I2I3)
But since vo=0 and ΖL isnt =0 that means I2 = 0 so the last equation becomes I1= (1a) *I3
Also Vo=v2=0 so V1= 0 too
lets go to the mesh current equations now
Vin=jωL * I1  jωL * I3
and
0= (jωL+Zx)*I3  jωL*I1
From these two equation what first came to my mind was this solution Zx=vin/I3 but this doesnt look acceptable
So i make the assumption that the secondary and primari of the transformer are actually shortcircuits and that makes Zx and jωL two parallel impedances so we have the following equation
Vin=jωL*I1=Zx*I3 =>
Zx= jωL*I1 / I3 and because I1=(1a)I3 we have
Zx=(1a)*jωL.
I have the feeling that i am missing something, maybe the assumption i made was wrong?
Your help will be much appreciated.
What we need to find is the value of Zx that will make Vo=0
So first i took the ideal transformer equations and had V2/v1 = a ( assuming that v2 and v1 are the voltages on the secondary and primary respectively
we also have i2/i1 = 1/a => i1=a*i2 or in mesh currents we have I1I3=a*(I2I3)
But since vo=0 and ΖL isnt =0 that means I2 = 0 so the last equation becomes I1= (1a) *I3
Also Vo=v2=0 so V1= 0 too
lets go to the mesh current equations now
Vin=jωL * I1  jωL * I3
and
0= (jωL+Zx)*I3  jωL*I1
From these two equation what first came to my mind was this solution Zx=vin/I3 but this doesnt look acceptable
So i make the assumption that the secondary and primari of the transformer are actually shortcircuits and that makes Zx and jωL two parallel impedances so we have the following equation
Vin=jωL*I1=Zx*I3 =>
Zx= jωL*I1 / I3 and because I1=(1a)I3 we have
Zx=(1a)*jωL.
I have the feeling that i am missing something, maybe the assumption i made was wrong?
Your help will be much appreciated.
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