Using Ohm's law, what is the electrical resistance (in ohms) of a component if a current of 0.1 A flows through it when a potential difference of 5 V is applied across its ends?

Introduction / Context:
Ohm's law is a fundamental relationship in electric circuits that connects voltage, current, and resistance. It is commonly written as V = I * R, where V is potential difference, I is current, and R is resistance. This question gives you the voltage and current for an electrical component and asks you to calculate its resistance. Such numerical applications of Ohm's law are common in school level physics and competitive exams.

Given Data / Assumptions:

• Potential difference V across the component is 5 V.
• Current I flowing through it is 0.1 A.
• The relationship between V, I, and R follows Ohm's law.
• We assume the component behaves like an ohmic resistor with constant resistance.

Concept / Approach:
Ohm's law states that the potential difference across a conductor is directly proportional to the current flowing through it, provided temperature and other physical conditions remain constant. Mathematically, V = I * R. If you know any two of the three quantities, you can rearrange the formula to find the third. In this problem, we need to find R, so we rearrange to R = V / I. Substituting the given values of V and I will give the resistance in ohms. This is a straightforward single step substitution problem, typical of easy numerical questions in electricity.

Step-by-Step Solution:
Step 1: Write down Ohm's law in the form V = I * R.Step 2: Rearrange the formula to solve for resistance: R = V / I.Step 3: Substitute the given values, V = 5 V and I = 0.1 A.Step 4: Compute R = 5 / 0.1 = 5 / (1 / 10) = 5 * 10 = 50 ohm.Step 5: Conclude that the resistance of the component is 50 ohm.

Verification / Alternative check:
You can verify the result by reversing the calculation. If the resistance is 50 ohm and the current is 0.1 A, then according to Ohm's law, the voltage should be V = I * R = 0.1 * 50 = 5 V, which matches the given potential difference. This consistency check confirms that the calculation is correct. Additionally, thinking about the numbers, a small current of 0.1 A flowing under a modest voltage of 5 V suggests a resistance significantly larger than 1 ohm, making 50 ohm a reasonable value.

Why Other Options Are Wrong:
A resistance of 0.5 ohm, option A, would give V = I * R = 0.1 * 0.5 = 0.05 V, which is much smaller than 5 V and therefore incorrect. A resistance of 100 ohm, option B, would give V = 0.1 * 100 = 10 V, which does not match the given 5 V. A resistance of 1 ohm, option D, would produce V = 0.1 * 1 = 0.1 V, again inconsistent with the data. Only 50 ohm leads back to the given voltage when combined with the stated current.

Common Pitfalls:
One common mistake is to divide I by V instead of V by I, leading to an incorrect value of resistance. Another error is mishandling decimal numbers such as 0.1, where students might incorrectly compute 5 / 0.1 as 0.5 instead of 50. To avoid such errors, remember that dividing by 0.1 is the same as multiplying by 10. Writing out the rearranged formula carefully before substituting the numbers helps ensure you are performing the correct operation in Ohm's law problems.

Final Answer:
50 ohm