Without using a calculators circuit analysis or Laplace tran

Without using a calculator\'s circuit analysis or Laplace transform, determine the following for the circuit. The transformer is ideal.

X_C, X_L, Z_TH, V_TH, Z_LOAD for maximum power transfer.

Solution

from the circuit w=377

xc=1/(jwc)=1/(j377*0.001)=-j2.6525 ohms

xl=jwl=j377*0.05=j18.85 ohms

transformation ratio k=(4/1)=4

convert all the parameters to primary side.

the secondary side reactance is converted to primary side. so, it becomes xl\'

xl \'=xl/k^2

xl \'=j18.85/16=j1.178 ohms

zth=3+j1.178-j2.6525=( 3-j1.4745) ohms

maximum power is transferred when zl= conjugate of zth=(3+j1.4745) ohms