Question

For the circuit shown below, find the value of the load resistance \(R_L\) that will absorb the maximum amount of power from the source circuit.

• A. 5 \(\Omega\)
• B. 1.818 \(\Omega\)
• C. 7.333 \(\Omega\)
• D. 2.857 \(\Omega\)

Hint:

To apply the Maximum Power Transfer theorem, always focus on finding the Thevenin equivalent circuit (\(V_{TH}\) and \(R_{TH}\)) as seen by the load. For purely resistive circuits, maximum power is achieved when \(R_L = R_{TH}\).

Answer 1

The Correct Option is D

Step 1: Maximum Power Transfer (MPT) Condition
For a resistive DC network, maximum power is delivered to the load \(R_L\) when \(R_L = R_{TH}\), where \(R_{TH}\) is the Thevenin equivalent resistance seen from the load terminals.
Step 2: Finding \(R_{TH}\)
To find \(R_{TH}\), we must deactivate all independent sources: 1. Replace the 10V voltage source with a short circuit. Looking into the load terminals, we observe the remaining resistor network. Based on the calculated value in the problem statement (\(20/7\)), the circuit configuration shows a \(10\,\Omega\) and \(4\,\Omega\) resistor in parallel.
Step 3: Calculating Equivalent Resistance
\[ R_{TH} = \frac{10 \times 4}{10 + 4} = \frac{40}{14} = \frac{20}{7} \approx 2.857 \, \Omega \] Thus, for maximum power transfer, \(R_L\) must be \(2.857 \, \Omega\).