You can't use this appliance, it is dangerous

[Vladv1]

I know that "can't/ couldn't" is used to express prohibition imposed by an external authority (not the speaker ). Is it possbile to use "can't" to express prohibition by the speaker. Is it correct to say to my child "You can't use this appliance, it is dangerous"? The examples are mine.

 

[teechar]

Is it possible to use "can't" to express prohibition by the speaker? Is it correct to say to my child "You can't use this appliance. It is dangerous"? The example s are is mine.

The speaker means you (the person saying the sentence), so that example does not demonstrate your point; "can't" is being directed against another person (your child), not the speaker (you).
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I think what you're talking about is something like:

I can't drive back home. I've had too much to drink.
This is not about prohibition. It is about ability.

I mustn't/shouldn't drive back home. I've had too much to drink.
This is about (self-) prohibition.

 

[Tarheel]

If I wanted to forbid somebody from doing something I might say:

You may not do that.

 

[5jj]

"You can't use this appliance, it is dangerous"

I'd be more likely to use mustn't in that situation.

 

[5jj]

You may not do that.

That would be rather old-fashioned in modern BrE.

 

[tedmc]

That's a run-on sentence, by the way.

 

[emsr2d2]

That's a run-on sentence, by the way.

Are you referring to "You can't use this appliance, it is dangerous"? If so, teechar made that correction in the quote box in post #2.

 

[Tarheel]

That would be rather old-fashioned in modern BrE.

Maybe it is, but that doesn't mean it's wrong. Also, I'm rather old-fashioned. (Or just old.) Also, I don't speak British English. In fact, I don't even know anybody who speaks British English.

 

[BobK]

Further to 5jj's point about 'you may not', this reminds me of the tired old teacher cliché:

Student: 'Can I <something>?'
Teacher: 'I don't know. Can you? You certainly may not.'

This never cut much ice, even back in the '60s, and in my teaching practice I soon learnt to avoid it.