首先说明的是，句中用 turn off the gas 是完全正确的，它的意思就是“关掉煤气”。

英语也可以说 turn off the stove（关掉炉子）。如下面两句均摘自朗文词典：

Can you turn off the stove?

I’m certain that I turned off the stove.

你的联想是对的，英语可以说 turn off the TV, turn off the light，也可以说 turn off the electricity（切断电源），但后者只是笼统地表示“切断电源”（尤其指切断某处的总电源）。如：

You should have had the sense to turn off the electricity first. 你应该知道要先关掉电源这个道理。

They turned off the electricity in the house when they left. 他们离开房子时把电源切断了。

They turned off the electricity in the house when they went away for their holiday. 他们外出度假时，切断了屋里的电源。

As an extra precaution, I turned off the electricity. 作为额外的防范措施，我把电路切断了。