The source impedance is ZS = (9 + j6) Ω in the circuit shown below. The maximum real power is transferred to the load impedance (ZL) when ZL is equal to:

F2 Vinanti Engineering 09.01.23 D3

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  1. 9 Ω
  2. the source impedance
  3. 6 Ω
  4. (9-j 6) Ω

Answer (Detailed Solution Below)

Option 4 : (9-j 6) Ω
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Detailed Solution

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Maximum power transfer theorem

Case 1: For AC circuit

In the case of AC voltage sources, maximum power flows from the source to load only if the load impedance’s value is equivalent to the complex conjugate of the thevenin's impedance.

\(Z_L=Z_{s}^{*}\)

Case 2: For the DC circuit

In the case of DC voltage sources, maximum power flows from the source to load if the resistance of the given load must be equal to the thevenin's resistance.

\(R_L=R_{s}\)

Calculation

F2 Vinanti Engineering 09.01.23 D3

Given, Zs = 9 + j6

The value of load impedance is given by:

\(Z_L=Z_{s}^{*}=({9+j6})^{*}\)

During conjugate operation, the sign of the imaginary part changes.

\(Z_L={9-j6}\)

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