Understanding Error Propagation in Resistance Measurement

Resistance $R$ is calculated using Ohm's Law:

$R=\frac{V}{I}$

Where:

• $V$ = Voltage (with ±3% error)
• $I$ = Current (with ±3% error)

Step-by-Step Solution:

Step 1: Identify the formula for percentage error in division

For $R=\frac{V}{I}$, the percentage error is:

$\frac{\Delta R}{R}\times 100\%=\left(\frac{\Delta V}{V}+\frac{\Delta I}{I}\right)\times 100\%$

Step 2: Substitute the given percentage errors

$\frac{\Delta R}{R}\times 100\%=3\%+3\%=6\%$

Final Answer: The error in the value of resistance is 6%

Related Topics:

• Error Analysis and Propagation
• Ohm's Law and Electrical Measurements
• Percentage Error Calculations
• Experimental Physics Techniques

Important Formulae:

For $R=\frac{V}{I}$:

$\frac{\Delta R}{R}=\frac{\Delta V}{V}+\frac{\Delta I}{I}$

Theory: When two quantities with errors are divided, the relative errors add up. This is because the derivative of the quotient shows that both errors contribute to the final uncertainty proportionally.