Understanding Potential Difference Calculation

This problem asks us to find the potential difference across a resistor when we know its resistance and the current flowing through it. This is a classic application of Ohm's Law, a fundamental principle in electrical circuits.

Applying Ohm's Law to Find Voltage

Ohm's Law describes the relationship between voltage (potential difference), current, and resistance in an electrical circuit. It is stated as:

\[V = I \times R\]

Where:

• \(V\) is the potential difference (voltage) measured in Volts (V).
• \(I\) is the current measured in Amperes (A).
• \(R\) is the resistance measured in Ohms (\(\Omega\)).

Given Values and Units Conversion

We are given the following values:

• Resistance (\(R\)) = 2.5 k\(\Omega\)
• Current (\(I\)) = 2 mA

Before we can use Ohm's Law, we need to ensure all units are in their base SI forms (Ohms for resistance, Amperes for current). The given values are in kiloohms (k\(\Omega\)) and milliamperes (mA), so we need to convert them:

• 1 k\(\Omega\) = \(10^3 \Omega\)
• 1 mA = \(10^{-3}\) A

Converting the given values:

• Resistance \(R = 2.5 \text{ k}\Omega = 2.5 \times 10^3 \Omega\)
• Current \(I = 2 \text{ mA} = 2 \times 10^{-3} \text{ A}\)

Step-by-Step Potential Difference Calculation

Now that we have the resistance and current in the correct units, we can calculate the potential difference (\(V\)) using Ohm's Law:

\[V = I \times R\]

Substitute the converted values into the formula:

\[V = (2 \times 10^{-3} \text{ A}) \times (2.5 \times 10^3 \Omega)\]

Multiply the numerical parts and the powers of ten separately:

\[V = (2 \times 2.5) \times (10^{-3} \times 10^3) \text{ V}\]

\[V = 5 \times 10^{(-3 + 3)} \text{ V}\]

\[V = 5 \times 10^0 \text{ V}\]

Since \(10^0 = 1\):

\[V = 5 \times 1 \text{ V}\]

\[V = 5 \text{ V}\]

The potential difference across the 2.5 k\(\Omega\) resistance is 5 V.

Conclusion: Potential Difference Result

Based on the calculation using Ohm's Law, the potential difference across the resistance is 5 Volts. This matches one of the provided options for the potential difference.

Revision Table: Key Formulas and Units

Additional Information: Understanding Ohm's Law and Units

Ohm's Law is a linear relationship between voltage and current for many materials, especially conductors like metals, under constant temperature. It essentially states that the current through a conductor between two points is directly proportional to the voltage across the two points and inversely proportional to the resistance between them.

Understanding unit prefixes like 'kilo' (k) and 'milli' (m) is crucial in physics and engineering calculations. They represent powers of 10:

• kilo (k) means \(10^3\) (one thousand)
• milli (m) means \(10^{-3}\) (one thousandth)

Always convert values with prefixes to the base unit before performing calculations using formulas like Ohm's Law to avoid errors.