Question:
In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\).
\begin{center}
\includegraphics[width=8cm]{62.png}
\end{center}
In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\).
\begin{center}
\includegraphics[width=8cm]{62.png}
\end{center}
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To apply the maximum power transfer theorem, calculate the Thevenin resistance by simplifying the circuit from the load's perspective. Ensure the load resistance matches \(R_{{Thevenin}}\) for optimal power transfer.
Updated On: Jan 31, 2025
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Solution and Explanation
Step 1: Apply the maximum power transfer theorem.
According to the maximum power transfer theorem, the load resistance \(R_L\) must be equal to the Thevenin resistance \(R_{{Thevenin}}\) of the circuit for maximum power to be delivered to the load: \[ R_L = R_{{Thevenin}}. \] Step 2: Determine \(R_{{Thevenin}}\).
Simplify the given circuit by removing the load and calculating the Thevenin resistance seen across the load terminals. After simplifying, the effective resistance is found to be: \[ R_{{Thevenin}} = 2.5 \, \Omega. \] Final Answer: \[ \boxed{2.5 \, \Omega} \]
According to the maximum power transfer theorem, the load resistance \(R_L\) must be equal to the Thevenin resistance \(R_{{Thevenin}}\) of the circuit for maximum power to be delivered to the load: \[ R_L = R_{{Thevenin}}. \] Step 2: Determine \(R_{{Thevenin}}\).
Simplify the given circuit by removing the load and calculating the Thevenin resistance seen across the load terminals. After simplifying, the effective resistance is found to be: \[ R_{{Thevenin}} = 2.5 \, \Omega. \] Final Answer: \[ \boxed{2.5 \, \Omega} \]
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