## Core Concept
The external laryngeal nerve is a branch of the superior laryngeal nerve, which in turn is a branch of the vagus nerve (cranial nerve X). The external laryngeal nerve primarily provides motor innervation to one of the intrinsic muscles of the larynx.

## Why the Correct Answer is Right
The external laryngeal nerve supplies the **cricothyroid muscle**. This muscle is one of the intrinsic muscles of the larynx and is responsible for tensing the vocal cords, thereby increasing the pitch of the voice. The cricothyroid muscle is unique among the intrinsic laryngeal muscles because it is the only one that is innervated by the external laryngeal nerve; all the other intrinsic muscles are innervated by the recurrent laryngeal nerve.

## Why Each Wrong Option is Incorrect
* **Option A:** This option is incorrect because the specific muscle supplied by the external laryngeal nerve is not listed; however, based on the correct answer, we know it is not this option.
* **Option B:** This option is incorrect for similar reasons; without the specific muscle listed, we infer it's not the cricothyroid muscle.
* **Option C:** This option might list another intrinsic muscle of the larynx, but it is incorrect because it is not the muscle supplied by the external laryngeal nerve.
* **Option D:** This option is incorrect because, like the others (excluding the correct answer), it does not accurately represent the cricothyroid muscle.

## Clinical Pearl / High-Yield Fact
A key point to remember is that the external laryngeal nerve is at risk during surgical procedures in the neck, such as thyroid surgery. Injury to this nerve can lead to voice changes due to the denervation of the cricothyroid muscle.

## Correct Answer: C. Cricothyroid muscle