Question

The resistance R = V/I where V = (50 ± 5)V and I = (10 ± 0.2)A. Find the percentage error in R​

Answer 1

Answer:

you just have to apply the basic formula of percentage error

hope you will find it usefull

Answer 2

Given:

• V = (50 ± 5)V
• I = (10 ± 0.2)A

To Find:

• Percentage error in R.

Solution:

We know,

• R = V/I [According to Ohm's law]

Now,

The Physical Quantity R will be given by:

• $\sf{\dfrac{\Delta R}{R} = \dfrac{\Delta V}{V} + \dfrac{\Delta I}{I}}$

Therefore,

$\sf{\dfrac{\Delta R}{R} = \pm\bigg(\dfrac{5}{50} + \dfrac{0.2}{10}\bigg)}$

Multiplying both sides with 100:

$\sf{\dfrac{\Delta R}{R} \times 100 = \pm \bigg(\dfrac{5}{50} + \dfrac{0.2}{10}\bigg) \times 100}$

$= \sf{\dfrac{\Delta R}{R} \times 100 = \pm \bigg(\dfrac{5}{50} \times 100 + \dfrac{0.2}{10} \times 100 \bigg)}$

$= \sf{\dfrac{\Delta R}{R} \times 100 = \pm \bigg(\cancel{\dfrac{5}{50}} \times 100 + \dfrac{0.2}{\cancel{10}} \times \cancel{100} \bigg)}$

$= \sf{\dfrac{\Delta R}{R} \times 100 = \pm (10 + 2)}$

⇒% error in R = ±12%

∴ The % error in quantity r is ±12%.

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More Information:

Percentage Error:

» Suppose a quantity A has measured value as (A ± ∆A) then the Percentage error in this quantity will be given by:

• $\sf{\dfrac{\Delta Z}{Z} \times 100 = \dfrac{\Delta A}{A} \times 100}$

Where ∆A is the error in quantity A.

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