Question

The maximum percentage error in the equivalent resistance of two parallel connected resistors of 100 ohm and 900 ohm, with each having a maximum 5% error, is:

• A. 3%
• B. 5%
• C. 10%
• D. 6%

Hint:

In parallel resistances, the maximum percentage error in the equivalent resistance is approximately equal to the largest individual error.

Answer 1

The Correct Option is B

Step 1: When resistors are connected in parallel, the equivalent resistance \( R_{\text{eq}} \) is given by: \[ \frac{1}{R_{\text{eq}}} = \frac{1}{R_1} + \frac{1}{R_2} \] For \( R_1 = 100 \) ohms and \( R_2 = 900 \) ohms, the equivalent resistance is: \[ R_{\text{eq}} = \frac{1}{\left(\frac{1}{100} + \frac{1}{900}\right)} \approx 90.91 \, \text{ohms} \]
Step 2: The percentage error in the equivalent resistance due to the maximum percentage error in the individual resistors is calculated using the formula for the propagation of errors. For parallel resistors, the maximum percentage error is approximately the same as the maximum error in either of the resistors. Therefore, the maximum percentage error in \( R_{\text{eq}} \) is 5%.
Thus, the maximum percentage error in the equivalent resistance is 5%.