Exams › GATE › Engineering Mathematics

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

1. 3
2. 4
3. 5
4. 7

Correct answer: 5

Solution

For maximum power transfer to a purely resistive load, the load resistance should equal the magnitude of the source internal impedance. Here, \(|4+j3|=\sqrt{4^2+3^2}=5\,\Omega\).

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
• 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
• 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 →