المولد متاح، وضوء الطوارئ يضيء الغرفة.

In present-tense Arabic, a sentence like المولد متاح usually does not use a separate word for is.

So:

• المولد = the generator
• متاح = available

Together, they mean The generator is available.

This is called a nominal sentence in Arabic.
If you wanted a past or future meaning, Arabic would use other words, but for simple present is/am/are, nothing is normally written.

Because Arabic is often written without short vowels, المولد can be read in more than one way. In this sentence, because the meaning is generator, it is read as:

• المُوَلِّد = al-muwallid = the generator

This is a very common issue in Arabic: the spelling stays the same, and context tells you which reading is correct.

So here, the intended word is المُوَلِّد and not another possible reading.

Because المولد is a masculine singular noun, the adjective/predicate must match it.

• المولد = masculine singular
• متاح = masculine singular available

If the noun were feminine, you would use:

• متاحة = feminine singular

For example:

• الخدمة متاحة = The service is available

So متاح matches المولد correctly.

In a sentence like المولد متاح, the first noun is definite, and the predicate is usually indefinite.

So:

• المولد = the generator
• متاح = available

This is the normal pattern for X is Y in Arabic.

If you made both parts definite, it would usually no longer sound like a simple The generator is available statement. So متاح without الـ is the expected form here.

ضوء الطوارئ is an iḍāfa construction, often called a genitive/possessive construction.

Literally, it is something like:

• ضوء = light
• الطوارئ = emergencies / emergency

So the phrase means:

• emergency light
• literally: the light of emergency/emergencies

Important things about iḍāfa:

• The first noun usually does not take الـ.
• The second noun is often definite here: الطوارئ.
• The whole phrase can be definite because the second part is definite.

That is why Arabic says ضوء الطوارئ, not الضوء الطوارئ.

This is just how Arabic commonly expresses the idea.

• الطوارئ literally relates to emergencies
• but in phrases like ضوء الطوارئ, it functions naturally as emergency in English

Arabic often uses established expressions that do not match English word-for-word. Similar examples include:

• قسم الطوارئ = emergency department
• حالة الطوارئ = state of emergency

So even though الطوارئ is plural in form, the overall phrase ضوء الطوارئ is the normal way to say emergency light.

The verb يضيء agrees with ضوء الطوارئ.

The head noun of that phrase is:

• ضوء = light

And ضوء is:

• singular
• masculine

So the verb is also singular masculine:

• يُضيء = it lights / it illuminates

In other words:

• ضوء الطوارئ يضيء الغرفة = The emergency light illuminates the room

The verb is agreeing with light, not with الطوارئ.

Because it is the thing being illuminated.

• يضيء = illuminates / lights
• الغرفة = the room

So the room is the direct object of the verb.

With full case endings, it would be:

• الغرفةَ in the accusative

A fully vowelled version of the second clause would be:

• وضوءُ الطوارئِ يضيءُ الغرفةَ

Here:

• ضوءُ = nominative, as the subject
• يضيءُ = verb
• الغرفةَ = accusative, as the direct object

Arabic allows more than one word order.

Here you have:

• ضوء الطوارئ يضيء الغرفة

This is basically subject + verb + object.

Arabic also often uses verb-first order, so you could also see:

• يضيء ضوءُ الطوارئ الغرفةَ

Both are possible in MSA.
The version in your sentence starts with ضوء الطوارئ to present the subject first, which can sound clearer or slightly more emphatic.

So this sentence is perfectly normal Arabic, even though many learners first meet Arabic as mainly verb-first.

Yes, ضوء is a word many learners find tricky.

It is pronounced approximately:

• ḍawʾ

Key points:

• ض is an emphatic d-like sound
• و here helps form the aw sound
• ء is a hamza, a glottal stop, like a brief catch in the throat

In context, with case ending, it would be:

• ضوءُ = ḍawʾu

So:

• ضوء الطوارئ ≈ ḍawʾu ṭ-ṭawāriʾi

The word may look small, but it contains a real final hamza, so do not pronounce it as if it were just ḍaw.

A fully vowelled version is:

المُوَلِّدُ مُتاحٌ، وضَوْءُ الطَّوارِئِ يُضيءُ الغُرْفَةَ.

Breakdown:

• المُوَلِّدُ = the generator
• مُتاحٌ = available
• وَ = and
• ضَوْءُ الطَّوارِئِ = the emergency light
• يُضيءُ = illuminates / lights
• الغُرْفَةَ = the room

Notice also:

• الطوارئ begins with ط, which is a sun letter, so ال is pronounced with assimilation: aṭ-ṭawāriʾi, not al-ṭawāriʾi.

Not necessarily.

متاح usually means:

• available
• accessible
• ready for use

So المولد متاح means the generator is available, but it does not automatically mean that it is currently switched on or operating.

If you specifically wanted the generator is on/running, Arabic might use a different expression depending on context.

So the sentence suggests:

• the generator is available
• and the emergency light is lighting the room

But متاح by itself does not guarantee that the generator is already running.