To solve the problem regarding the surge current rating of an SCR (Silicon Controlled Rectifier) and determine the correct answer, we need to explore the given options separately:

1. Understanding Half Cycle and Full Cycle Surge Current Ratings:
   • The given half cycle surge current is 3000 A for a 50 Hz supply. This means the peak current the SCR can handle for half of a 20 ms (1/50 Hz) cycle is 3000 A.
   • One cycle refers to a complete 20 ms duration, equivalent to two half cycles.
   • The one cycle surge current rating can be calculated using the peak value divided by √2, because a cycle involves both half cycles.
2. \(I_{\text{full cycle}} = \frac{I_{\text{half cycle}}}{\sqrt{2}} = \frac{3000}{\sqrt{2}} = 2121.32 \, \text{A}\)
3. From this calculation, option A, which states the one-cycle surge current as 2121.32 A, is correctly determined.
4. Calculating the I²t Rating:
   • I²t is an important parameter that represents the energy (current squared over time) the SCR can withstand without damage during a fault condition.
   • I²t for one cycle can be calculated as follows:
5. \(I^{2}t = I_{\text{half cycle}}^{2} \times \frac{T}{2} = (3000)^2 \times \frac{1}{100} = 45000 \, \text{Amp}^{2}\text{s}\)
6. Hence, option C, asserting that I²t rating = 45000 Amp²s, is correct.

Based on these calculations, the correct choices are:

• Option A: One cycle surge current = 2121.32 A
• Option C: I²t rating = 45000 Amp²s

Thus, the correct answer from the given options is A and C only.