My throat is dry after sleeping with the AC on＝エアコンを付けて寝たから喉が乾燥している
AC＝Air Conditioner＝エアコン
Dryは「乾燥している」ですが、「すごく乾燥している」と表現したい時は「parched」や「dehydrated」などのもっと強い言葉を使いましょう。
"My throat is dry because I slept with the air conditioner on."
"My throat is dry after sleeping with the air conditioner on"
In order to explain to someone that your throat is dry as a result of sleeping with the air conditioner on, you can say "My throat is dry because I slept with the air conditioner on" or "My throat is dry after sleeping with the air conditioner on". Both these sentences explain how and why your throat is sore to the person you are wanting to tell.
「エアコンをつけたまま寝たので喉が乾燥している」は、次のように言えます。
"My throat is dry because I slept with the air conditioner on"（エアコンをつけたまま寝たので喉が乾燥している）
"My throat is dry after sleeping with the air conditioner on"（エアコンをつけたまま寝たので喉が乾燥している）
どちらの文も、なぜ、またどのようにのどが痛いのか伝えています。
The AC made my throat dry as I unintentionally left it on
If you wish to state that your throat is dry because you left the air conditioner on, then you may try one of the two above exampled sentences.
If you do something that you do not mean to do, then it is described as being an 'unintentional' action.
The air conditioning in my room has dried up my airways during the night.
This answer perfectly describes the issue. You have slept with the air conditioning on, and hence this has lead to the air in your room becoming very dry. When you breath in this dry air it can cause dehydration and therefore dry out your throat, which is part of your airways into your lungs.
When something 'dries up' it means that the moisture has dispersed.
I slept with the air conditioner on and it caused my dry throat.
After sleeping with the AC on, I got a dry throat.
Any one of these sentences can be used:-
1. I slept with the air conditioner on and it caused my dry throat.
私はエアコンをつけて眠り、それが私の乾いた喉を引き起こしました。
Watashi wa eakon o tsukete nemuri, sore ga watashi no kawaita nodo o hikiokoshimashita.
2. After sleeping with the AC on, I got a dry throat.
ACをオンにして寝た後、私は喉が乾いた。
AC o on ni shite neta nochi, watashi wa nodo ga kawaita.
これらどちらの文もこの状況で使うことができます。
1. I slept with the air conditioner on and it caused my dry throat.
（エアコンをつけたまま寝たので、喉が乾燥してしまいました）
2. After sleeping with the AC on, I got a dry throat.
（エアコンをつけたまま寝たので、喉が乾燥してしまいました）
The AC made my throat dry as I unintentionally left it on
If you wish to state that your throat is dry because you left the air conditioner on, then you may try one of the two above exampled sentences.
If you do something that you do not mean to do, then it is described as being an 'unintentional' action.
My throat is dry thanks to sleeping with the AC on.
My throat is dry because I slept with the AC on.
It is natural to shorten "air conditioner" to "AC" in modern English. You can substitute "on" for "going" or "running" because the air conditioner is a machine. For example: "I slept with the AC running," is also OK.
My throat is dry thanks to sleeping with the AC on.
English speakers will sometimes use the phrase "thanks to" as a lighthearted way to express that something has caused a problem. For example: "Thanks to the rain, the event was cancelled."
My throat is dry because I slept with the AC on.（エアコンをつけたまま寝たので喉が乾燥している）
現代の英語では "air conditioner" を "AC" と省略するのは自然です。エアコンは機械なので、"on" の代わりに "going" または "running" も使えます。
例えば、"I slept with the AC running" でもオッケーです。
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My throat is dry thanks to sleeping with the AC on.（エアコンをつけたまま寝たので喉が乾燥している）
英語では、何かによって問題が生じたことを陽気に表すときに、"thanks to" が使われることがあります。
"Thanks to the rain, the event was cancelled."
（雨のおかげで、イベントが中止になった）
アメリカ合衆国 
イギリス 
カナダ 
