Cessna 210 instructor reported an electrical failure and landing gear malfunction during initial climb on a training flight in visual conditions. The instructor lowered the gear by the alternate system and landed safely.

Narrative

I was training an Instrument/Private student in a Cessna 210; looking to gain hours for commercial and a complex endorsement. While on the ground; all systems were normal. During the takeoff initial climb; I looked at the ammeter and it was showing the needle to the left. I thought strange and reminded myself to check in a few seconds after we were safely off the ground. We did retract the gear. within a few more seconds; the Garmin 530 flickered and went off. I was going to enter a squawk code; then the transponder went blank. We very quickly lost all power. I called the Tower on my cell phone; connected via bluetooth to my headset. They answered and worked with us to make it safely back to the ground; they did a great job. We took off XX; turned down wind and planned to land. The gear didn't extend; so we flew crosswind and upwind to manually pump down the gear. The Tower verified it was down. From there we returned to XX and landed without incident. It ended well and I think all parties involved did a great job. Our mechanic has already investigated the incident and found it was the voltage regulator that was faulty; a new one has been ordered.