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Complex Conjugate Load Matching

For the circuit shown in Fig. Q40, what should be the value of load impedance to be connected across terminals ‘a’ and ‘b’, for the maximum power transfer from the circuit. Fig. Q40
Original source figure for BMS Electrical question 40
Original figure referenced in question 40.
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Answer & Explanation
Correct AnswerB. 4j Ω

Quick Explanation

For maximum average power in AC, the load must equal the complex conjugate of the Thevenin impedance. With the independent voltage source suppressed, the impedance seen at a-b is (−j2)||(j4)=−j4 Ω, so the required load is +j4 Ω.

Formula / Key Relation

ZL=Zth*; Zth=(−j2)||(j4)=−j4Ω ⇒ ZL=+j4Ω
Complex Conjugate Load Matching explanatory diagram

Detailed Explanation

Correct Answer

B — 4j Ω

Concept and Reasoning

For maximum average power in AC, the load must equal the complex conjugate of the Thevenin impedance. With the independent voltage source suppressed, the impedance seen at a-b is (−j2)||(j4)=−j4 Ω, so the required load is +j4 Ω.

Calculation / Key Relation

ZL=Zth*

Zth=(−j2)||(j4)=−j4Ω ⇒ ZL=+j4Ω

Exam Takeaway

AC maximum power transfer uses conjugate matching.

Common Mistake

Do not set ZL=Zth when Zth is complex; take the conjugate.

Quick Trick

AC maximum power transfer uses conjugate matching.

Common Mistake

Do not set ZL=Zth when Zth is complex; take the conjugate.

Exam Tip

AC maximum power transfer uses conjugate matching.

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