A single phase $10$ kVA, $50$ Hz transformer with $1$ kV primary winding draws $0.5$ A and $55$ W, at rated voltage and frequency, on no load. A second transformer has a core with all its linear dimensions $\sqrt{2}$ times the corresponding dimensions of the first transformer. The core material and lamination thickness are the same in both transformers. The primary windings of both the transformers have the same number of turns. If a rated voltage of $2$ kV at $50$ Hz is applied to the primary of the second transformer, then the no load current and power, respectively, are
1. $0.7$ A, $77.8$ W
2. $0.7$ A, $155.6$ W
3. $1$ A, $110$ W
4. $1$ A, $220$ W