Ohm's Law is a fundamental principle in electrical engineering that relates voltage (V), current (I), and resistance (R) in an electric circuit. Ohm's Law states that the voltage across a conductor is directly proportional to the current flowing through it, with the proportionality constant being the resistance of the conductor.
The mathematical expression for Ohm's Law is:
[tex]\[ V = I \cdot R \][/tex]
From this fundamental equation, we can rearrange the terms to solve for different quantities. To find the resistance (R), we can rearrange the equation as follows:
[tex]\[ R = \frac{V}{I} \][/tex]
Therefore, the correct statement of Ohm's Law when solving for resistance is:
[tex]\[ R = \frac{V}{I} \][/tex]
Let's check each option provided in the question:
A. [tex]\( R = V \cdot I \)[/tex]
This statement is incorrect because it does not correctly represent the relationship among voltage, current, and resistance. According to Ohm's Law, resistance is not the product of voltage and current.
B. [tex]\( R = \frac{I}{V} \)[/tex]
This statement is incorrect because it incorrectly places current in the numerator and voltage in the denominator. According to Ohm's Law, resistance is the ratio of voltage to current, not the other way around.
C. [tex]\( R = \frac{V}{I} \)[/tex]
This statement is correct. It accurately describes the relationship among voltage, current, and resistance as stated by Ohm's Law. Resistance (R) is indeed the ratio of voltage (V) to current (I).
D. [tex]\( V = \frac{I}{R} \)[/tex]
This statement is incorrect because it misrepresents the relationship among the quantities. According to Ohm's Law, voltage is the product of current and resistance, not the ratio of current to resistance.
Thus, the correct answer is:
C. [tex]\( R = \frac{V}{I} \)[/tex]
