Question

which of the following is dimensionless a​

Answer 1

Answer:

Answer is 6

Explanation:

Answer 2

Question :

The resistance R = V/I, where V = 100±4 volts and I = 10±0.1 amperes. What is the maximum percentage error in R....

A) 3%

B) 4%

C) 5%

D) 6%

Solution :

We are given that,

» Applied voltage = (100 ± 4) volts

» Current flow = (10 ± 0.1) amperes

From the given data,

• Magnitude of voltage (V) = 100
• Error in measurement of voltage (∆V) = 4
• Current flow (I) = 10
• Error in measurement of current = 0.1

We have to find percentage error in the measurement of resistance.

❖ If Z = A/B, then the maximum fractional error in Z is given by

$\dag\:\underline{\boxed{\bf{\purple{\dfrac{\Delta Z}{Z}=\dfrac{\Delta A}{A}+\dfrac{\Delta B}{B}}}}}$

Similarly maximum fractional error in measurement of R,

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

By substituting the given values;

$\sf:\implies\:\dfrac{\Delta R}{R}=\dfrac{4}{100}+\dfrac{0.1}{10}$

$\sf:\implies\:\dfrac{\Delta R}{R}=0.04+0.01$

$\sf:\implies\:\dfrac{\Delta R}{R}=0.05$

Percentage error in measurement of resistance;

$\sf:\implies\:\%\dfrac{\Delta R}{R}=0.05\times 100$

$:\implies\:\underline{\boxed{\bf{\gray{\%\dfrac{\Delta R}{R}=5\%}}}}$

∴ (C) is the correct answer!