The resistance R=V/I, where V = 100 ± 5.0 V and I = 10 ± 0.2A. What is the total error in R?

Step 1: Given Data

Voltage = 100 ± 5.0V

Current = 10 ± 0.2A

Step 2: Formula Used

 \({\triangle R \over R} = \pm ({\triangle V \over V} + {\triangle I \over I})\)

Step 3: Calculating the error in the resistance
 \({\triangle R \over R} = \pm ({\triangle 5 \over 100} + {\triangle 0.2 \over 10})\)
 \({\triangle R \over R} = \pm (0.05 +0.02)\)
 \({\triangle R \over R} = \pm 0.07\)
The percentage error will be

 \({\triangle R \over R} \times 100 = 0.07 \times 100 \)
 \({\triangle R \over R} \times 100 = 7\)%

The total percentage error in the resistance will be 7%.

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