Question

A potential difference V=(100+-2)volt when applied across a resistance R,gives a current I=(10+-0.5)ampere calculate percentage error in R .Given R=V/I.​

Answer 1

Question:

A potential difference V = (100 $\pm$ 2) volt when applied across a resistance R gives a current I = (10 $\pm$ 0.5) ampere. Calculate percentage error in R. Given R = V/I

Solution:

V= 100 $\pm$ 2 volt

I = 10 $\pm$ 0.5 ampere

Now, we will show the limits of errors in percentage errors,

$Percentage \ Error = \frac{|Actual \ Value - Expected \ Value|}{Expected \ Value} * 100 \% = \frac{|Error \ Value|}{Exact \ Value} * 100\%$

$V = 100 \pm \frac{2}{100} * 100 \% = 100 \pm 2 \%$

$I = 10 \pm \frac{0.5}{10} * 100 \% = 10 \pm 5 \%$

Now, we are given with R = V/I

Therefore,

Percentage Error in R = Percentage Error in V + Percentage Error in I

Percentage Error in R = 2% + 5%

Percentage Error in R = 7%

The percentage error in R is 7%