In the network shown below, maximum power is to be transferred to the load \(R_L\). The value of \(R_L\) (in \(\Omega\)) is \(\_\_\_\_\).
Show Hint
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.
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:
\[
\boxed{2.5 \, \Omega}
\]
