In the circuit, the maximum power that can be transferred to Load Z_L is

Calculation:

The given circuit is

\(\rm P_{ZL}=I^2_{rms}.Z_L\)

\(\rm I_{rms}=\frac{I_m}{√2}\)

Z_s = R_s + j ωL_s =  10 + j 1000 × 10 × 10^-3 = 10 + j 10 Ω 

\(\rm I_m=\frac{i(t)(10+j10)}{10+j10+Z_L}\)

As we know Z_L = Z_s* = 10 - j10 = R_L + j X_L

|Z_L| = 10√2 Ω 

\(\rm I_m=\frac{10√2(10+j10)}{10+j10+10-j10}\)

\(|I_m|=\frac{10√2×10√2}{20}=10\ \rm Amp\)

\(\rm I_{rms}=\frac{I_m}{√2}=\frac{10}{√2}\)

\(\rm P_{Z_L}=I^2_{rms}.Z_L=\left(\frac{10}{√2}\right)^2×10\)

P_ZL = 500 W

Important Points Maximum power transfer theorem for AC circuits:

The maximum power transfer theorem states that the maximum power flow through an AC circuit will occur when the load impedance is equal to the complex conjugate of the source impedance.

ZL = ZS* 

|ZL| = |ZS|

ZL = Load impedance

ZS = Source impedance

Important points: