Question

Resistance of a given wire is obtained by measuring the current flowing in it and the voltage differenceapplied across it. If the percentage errors in the measurement of the current and the voltage differenceare 3% each, then error in the value of resistance of the wire is

Answer 1

In multiplication or division, percentage errors are simply added
Since R=V/I

% error in R= % error in V + Percent error in I
                 = 3%+3%
                 = 6 %

Answer 2

The percentage error in resistance is 6%

Given data:

3 percent of error in both voltage and current

To find:

Percentage error in resistance = ?

Solution:

We need to apply the formula given below:

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

Where,

R is the resistance

V is the voltage

I is the current

$\frac{\Delta V}{V}=3 \%=\frac{3}{100}=0.03$

Similarly,

$\frac{\Delta I}{I}=0.03$

Therefore,

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

$\frac{\Delta R}{R}=0.03+0.03$

$\Rightarrow \frac{\Delta R}{R}=0.06$

Thereby, percentage error in resistance is,

$\frac{\Delta R}{R}=0.06 \times 100 \%=6 \%$