Q21GATE 2007MCQ

An independent voltage source in series with an impedance $Z_{s}=R_{s}+jX_{s}$ , delivers a maximum average power to a load impedance $Z_{L}$ when

🚀 Solve in Practice Mode

📖 Explanation

$Z_{L}=R_{s}-j X_{s}$ For maximum power transfer

\begin{array}{l} Z_{L}=Z_{S}^{*} \\ Z_{L}=R_{s}-j X_{s} \end{array}

Q22GATE 2007MCQ

For the circuit shown in the figure, the Thevenin voltage and resistance looking into X-Y are

🚀 Solve in Practice Mode

📖 Explanation

For $V_{\mathrm{Th}}$ , applying KCL at node X

\begin{aligned} 2&=\frac{V_{T h}}{2}+\frac{V_{T h}}{1}+\frac{V_{T h}-2 i}{1} \\ \text{where,}\qquad i&=\frac{V_{T h}}{1}\\ So \quad 2&=V_{\text {Th }}\left(\frac{1}{2}+\frac{1}{1}+\frac{1}{1}-\frac{2}{1}\right) \\ V_{\mathrm{Th}}&=4 V \end{aligned}

From the figure $I_{s c}=2 \mathrm{Amp}$ $\text{So }\quad R_{\mathrm{Th}}=\frac{V_{\mathrm{Th}}}{I_{S C}}=\frac{4}{2}=2 \Omega$

Q23GATE 2005MCQ

The maximum power that can be transferred to the load resistor $R_{L}$ from the voltage source in the figure is

🚀 Solve in Practice Mode

📖 Explanation

For maximum power transfer

\begin{aligned} R_{L}&= R_{s}=100 \Omega \\ \therefore \quad P_{\max }&=\frac{V^{2}}{R}=\frac{5 \times 5}{100}=0.25 \mathrm{W} \\ &\qquad\left(V \operatorname{across} R_{L}=5 \mathrm{V}\right) \end{aligned}

Q24GATE 2005MCQ

For the circuit shown in the figure, Thevenin's voltage and Thevenin's equivalent resistance at terminals a-b is

🚀 Solve in Practice Mode

📖 Explanation

For $V_{\mathrm{Th}}$ $\frac{V_{a b}}{5}+\frac{V_{a b}-10}{5}=1$ (when current source is in series with voltage source effect of current source is taken) $2 V_{a b}=15 \Rightarrow V_{a b}=7.5$ $\frac{0.5 I_{1}}{I_{1}}=\frac{5}{R} \Rightarrow R=10 \Omega$ (Impedance connected to $0.5 I_{1}$ current source) For $R_{\text {Th }}$ , Make independent sources dead, $R_{T h}=5 \| 5=2.5 \Omega$

Q25GATE 2003MCQ

A source of angular frequency 1 rad/sec has a source impedance consisting of 1 $\Omega$ resistance in series with 1 H inductance. The load that will obtain the maximum power transfer is