P$9\mathrm{.}76\_8$ed

A series combination ZL of a $150($Ohm$)$ resistor and a $20$ nF $($nano F$)$ capacitor is connected to a sinusoidal voltage source by a linear transformer.$$ The source is operating at a frequency of $500$ krad$/$sec$.$ At this frequency, the internal impedance of the source is ZS $=5+$ j $15($Ohm$).$ The rms voltage at the terminals of the source is $125$ Vrms when the source is not loaded.$$ The parameters of the linear transform are:

R$1=12($Ohm$)$L$1=80$H $($micro H$)$ R$2=50($Ohm$)$ L$2=500$H $($micro H$)$M $=100$H $($micro H$)$

a$)$ What is the value of the impedance reflected into the primary side?

$$ Zr $=$ Answer $1$ Question $5+$ j Answer $2$ Question $5($Ohm$)$

b$)$ What is the value of the impedance seen at the terminals ab of the source?

$$ Zab $=$ Answer $3$ Question $5+$ j Answer $4$ Question $5($Ohm$)$

CheckQuestion $5$

$$k $=$ Answer $1$ Question $4$

b$)$ What is the peak amplitude of i$1?$

$|$ i$1|=$ Answer $2$ Question $4$ A

Given vg $=369$ cos$(50,000$t$)$ V$.$

The coefficient of coupling k is adjusted until the peak amplitude of i$1$ is maximum.

$$a$)$ What is the value of k$?[$Hint: Use reflected impedance which includes k and determine when Zin is minimum which yields the max current$]$

$$k $=$ Answer $1$ Question $4$

b$)$ What is the peak amplitude of i$1?$

$|$ i$1|=$ Answer $2$ Question $4$ A

Given vg $=369$ cos$(50,000$t$)$ V$.$

The coefficient of coupling k is adjusted until the peak amplitude of i$1$ is maximum.

$$a$)$ What is the value of k$?[$Hint: Use reflected impedance which includes k and determine when Zin is minimum which yields the max current$]$

$$k $=$ Answer $1$ Question $4$

b$)$ What is the peak amplitude of i$1?$

$|$ i$1|=$ Answer $2$ Question $4$ A

Given:$$ L$1=5$ H$$ L$2=0\mathrm{.}2$ H$$ M $=0\mathrm{.}5$ H$$ R$0=10($Ohm$)$

$$ ig$=-10+$ e$-10$t$$A for$$ t $0$ i$2=0\mathrm{.}625$e$-10$t$0\mathrm{.}250$ e$-50$t$$A for$$ t $0$