Explanation:

In a single-phase half-wave thyristor circuit with R load, the thyristor is connected in series with the load and the AC supply. The thyristor conducts only for a part of the positive half-cycle of the AC wave, and the load current flows only during this time. The rest of the time, the thyristor is non-conducting and the load current is zero.

To calculate the power delivered to the resistive load, we can use the formula:

P = V(rms)^2 / R

where P is the power delivered to the load, V(rms) is the RMS voltage across the load, and R is the resistance of the load.

Now, let's break down each option and see which one is correct.

Option A: (average load voltage) x (average load current)

This formula is not correct because the load voltage and current are not constant. The thyristor conducts only for a part of the positive half-cycle, so the load voltage and current are not constant but vary with time.

Option B: (rms supply voltage)^2 / R

This formula is also not correct because the power delivered to the load depends on the load voltage, not the supply voltage. The supply voltage is not directly related to the power delivered to the load.

Option C: (rms load voltage)^2 / R

This formula is correct because the RMS voltage across the load is directly related to the power delivered to the load. The RMS voltage across the load is the effective voltage that produces the same amount of power as the AC voltage. Therefore, we can use this formula to calculate the power delivered to the load.

Option D: (average load voltage) / R

This formula is not correct because it does not take into account the fact that the load voltage and current are not constant. The load voltage and current vary with time, so we cannot use the average values to calculate the power delivered to the load.

Therefore, option C is the correct answer.

Conclusion:

The power delivered to the resistive load in a single-phase half-wave thyristor circuit with R load can be calculated using the formula P = (rms load voltage)^2 / R. This formula takes into account the fact that the load voltage and current vary with time and uses the effective voltage (RMS voltage) to calculate the power delivered to the load.