Exams › GATE › Engineering Mathematics

For maximum power transfer between two cascaded sections of an electrical network, the relationship between the output impedance $Z_1$ of the first section and the input impedance $Z_2$ of the second section is

1. $Z_2 = Z_1$
2. $Z_2 = -Z_1$
3. $Z_2 = Z_1^*$
4. $Z_2 = -Z_1^*$

Correct answer: $Z_2 = Z_1^*$

Solution

For maximum power transfer in AC networks, the impedance of the receiving section must be the complex conjugate of the output impedance of the driving section. This ensures that the real parts match and the reactive parts cancel, maximizing power delivered.

Related GATE Engineering Mathematics questions

• For a parallel RLC circuit, which one of the following statements is NOT correct?
• In the circuit shown, the switch \(S\) is open for a long time and is closed at \(t=0\). The current \(i(t)\) for \(t\ge 0^+\) is
• The transfer function \(V_2(s)/V_1(s)\) of the circuit shown below is
• A source \(v_s(t)=V\cos(100\pi t)\) has an internal impedance of \((4+j3)\,\Omega\). If a purely resistive load connected to this source has to extract the maximum power from the source, its value in \(\Omega\) should be
• The transfer function $\frac{V_2(s)}{V_1(s)}$ of the circuit shown below is [Series capacitor $100\,\mu$F from input to output node; from output node to ground a series branch of $10\,\text{k}\Omega$ resistor and $100\,\mu$F capacitor; output taken across the output node to ground.]
• The equivalent impedance \(Z_{eq}\) for the infinite ladder circuit shown in the figure is

⚔️ Practice GATE Engineering Mathematics free + battle 1v1 →