**Core Concept:**
The pudendal nerve is a mixed nerve that arises from the sacral plexus, specifically from S2, S3, and S4 spinal nerves. It supplies the muscles of the perineum, skin of the perineum, and the sphincter of the bladder. The sphincter of the bladder is a ring of smooth muscle fibers located at the neck of the bladder, which plays a crucial role in controlling the flow of urine from the bladder to the urethra.

**Why the Correct Answer is Right:**
The correct answer, C, refers to the root value of the pudendal nerve supplying the sphincter of the bladder, which is S3. S3 is one of the spinal nerves that form the sacral plexus and contributes to the formation of the pudendal nerve. The pudendal nerve carries both sensory and motor fibers, and S3 contributes to the formation of the motor fibers that innervate the sphincter of the bladder.

**Why Each Wrong Option is Incorrect:**
A, B, and D are incorrect because they represent root values for different spinal nerves that do not contribute to the formation of the pudendal nerve. A refers to S1, which is responsible for the genital and anal sphincters but not the sphincter of the bladder. B refers to S2, which is responsible for the muscles of the perineum but not the sphincter of the bladder. D refers to S4, which is responsible for the muscles of the perineum but not the sphincter of the bladder.

**Why the Correct Answer is Right:**
S3 is responsible for the formation of the motor fibers that innervate the sphincter of the bladder, making it the correct answer for the question. The sphincter of the bladder plays a critical role in controlling the flow of urine from the bladder to the urethra. Any disruption to this function can lead to urinary incontinence and other complications.

**Why Each Wrong Option is Incorrect:**
Root values S1, S2, and S4 are incorrect because they represent nerves responsible for different functions and not the formation of the pudendal nerve supplying the sphincter of the bladder. S1 is involved in the genital and anal sphincters, S2 is responsible for the muscles of the perineum, and S4 is related to the muscles of the perineum and anal sphincters but not the sphincter of the bladder.

**Clinical Pearls:**
Understanding the root values of the sacral nerves is crucial for understanding regional anatomy and physiology, particularly in the context of the urinary system. It is essential to recognize that different sacral nerves innervate different structures and functions. Any impairment or injury to these nerves can lead to various clinical conditions, including urinary incontinence.