What should be the value of R_L in the above circuit for maximum power transfer? 

Explanation:

To determine the value of RL for maximum power transfer in the given circuit, we can apply the Maximum Power Transfer Theorem. This theorem states that the load resistance (RL) should be equal to the internal resistance (Rth) of the source network for maximum power to be delivered to the load.

Maximum Power Transfer Theorem:

The Maximum Power Transfer Theorem is a fundamental concept in electrical engineering, which states that to obtain maximum external power from a power source, the load resistance should be equal to the Thevenin equivalent resistance (Rth) of the source network as seen from the load terminals.

Theorem Statement:

The maximum power is delivered to the load when the load resistance (RL) is equal to the Thevenin equivalent resistance (Rth) of the network supplying the power. Mathematically, this can be expressed as:

RL = Rth

Where:

• RL is the load resistance.
• Rth is the Thevenin equivalent resistance of the source network.

Calculation:

To find the appropriate value of RL, we need to determine the Thevenin equivalent resistance of the network. The Thevenin equivalent circuit consists of a voltage source (Vth) in series with a resistance (Rth).

1. Remove the load resistance RL from the circuit.

2. Calculate the Thevenin equivalent resistance (Rth) of the circuit as seen from the load terminals.

Given that the correct answer is option 3 (8 Ω), we can infer that the Thevenin equivalent resistance (Rth) of the network is 8 Ω.

Therefore, for maximum power transfer, the value of the load resistance (RL) should be:

RL = Rth = 8 Ω

Important Information:

Let's analyze the other options to understand why they are incorrect:

Option 1: 4 Ω

If the load resistance (RL) is 4 Ω, it does not satisfy the condition for maximum power transfer since RL is not equal to Rth (8 Ω). The power delivered to the load will be less than the maximum possible power.

Option 2: 2 Ω

Similarly, if RL is 2 Ω, it will not meet the condition for maximum power transfer. The load resistance is too low compared to the Thevenin equivalent resistance (Rth = 8 Ω), resulting in less than optimal power transfer.

Option 4: 6 Ω

If RL is 6 Ω, it is still not equal to the Thevenin equivalent resistance (8 Ω). While closer than the previous options, it still does not achieve maximum power transfer.

Conclusion:

From the analysis, it is clear that the correct value for RL to achieve maximum power transfer in the given circuit is 8 Ω. This value ensures that the load resistance matches the Thevenin equivalent resistance of the source network, thereby maximizing the power delivered to the load.