At the terminals of a network, to which a certain load is connected, it was found that Rth = 20 Ω and Vth = 80 V. The maximum possible power supplied to the load is:

Maximum Power Transfer Theorem:

The Maximum Power Transfer Theorem states that the maximum power is transferred to the load when the load resistance (R_L) is equal to the Thevenin equivalent resistance (R_th) of the network supplying the power. This theorem is critical in electrical and electronics engineering for optimizing power transfer in circuits.

Given Data:

• Thevenin Equivalent Resistance, R_th = 20 Ω
• Thevenin Equivalent Voltage, V_th = 80 V

To Find: The maximum possible power supplied to the load.

Solution:

To determine the maximum power delivered to the load, we use the formula for power in a resistive circuit:

P_max = (V_th)² / (4 × R_th)

Where:

• P_max is the maximum power delivered to the load.
• V_th is the Thevenin equivalent voltage.
• R_th is the Thevenin equivalent resistance.

Step-by-Step Calculation:

1. Substitute the given values of V_th and R_th into the formula:

P_max = (80)² / (4 × 20)

P_max = 6400 / 80

P_max = 80 W

Thus, the maximum possible power that can be supplied to the load is 80 W.

Important Information:

To analyze the other options, let us understand why they are incorrect:

Option 2: 40 W

This value is incorrect because it does not satisfy the condition for maximum power transfer. The maximum power is derived based on the condition that the load resistance equals the Thevenin resistance (R_L = R_th), and the calculated value from the given data is 80 W, not 40 W.

Option 3: 160 W

This value is incorrect because it represents twice the actual maximum power. The formula for maximum power transfer ensures that the power is limited by the resistive components in the circuit. 160 W exceeds the calculated value of 80 W, making it invalid.

Option 4: 4 W

This value is far too low and does not align with the given circuit parameters. The small value indicates a misunderstanding of the formula or incorrect substitution of values.

Conclusion:

The correct option is Option 1, as the maximum power delivered to the load, calculated using the Maximum Power Transfer Theorem, is 80 W. This result is consistent with the given circuit parameters and the principles of electrical engineering.