Question

The resistance $R = \dfrac{V}{I}$ where $V = (100 \pm 5)V$ and $I = (10 \pm 0.2)A$. The percentage error in R is?
A. 5.2%
B. 4.8%
C. 7%
D. 3%

Answer 1

Hint: \[\dfrac{{\Delta R}}{R} = \dfrac{{\Delta V}}{V} + \dfrac{{\Delta I}}{I}\] ,
Where R is the resistance and $\Delta R$ is the difference between measured quantity and actual value,
V is the potential difference and $\Delta V$ is between measured quantity and actual value,
I is the current and $\Delta I$ is the difference between measured quantity and actual value.

Complete step by step solution:
As we know that Measurement Error is the difference between measured quantity and its actual value.
There has always been instrumental error or other aspects of it like System failure, etc., but it leads to an error.
So, if we can calculate the error, then we will know how much error is there and then the measurement of our experiment will be more accurate.
There are three types of error, and for percentage error we will solve it by some other way.
Therefore, we will extract individual errors and then sum all of them.
Here,
Actual readings and the difference between measured reading and actual reading is given,

As we all know that error in percentage can never be negative and to calculate percentage error in R, we should multiply by 100 to our calculation as given below.
$\dfrac{{\Delta R}}{R} = \dfrac{{\Delta V}}{V} \times 100 + \dfrac{{\Delta I}}{I} \times 100$ ,
We are given,
$\Delta V = 5V$ and \[V = 100V\],
$\Delta I = 0.2A$ and $I = 10A$,
Now, Let’s put it in the equation to find out the percentage error in R.
$\dfrac{{\Delta R}}{R} = \dfrac{5}{{100}} \times 100 + \dfrac{{0.2}}{{10}} \times 100$ ,
After solving it,
We will get,
$\dfrac{{\Delta R}}{R} = 7$,
That is percentage error in R, $7\% $ .

$\therefore $ Option(C) is correct.

Note: Error can never be negative. Multiply by 100, when you have to find out the error percentage.