Question 143: Units , Dimensions and Error Analysis

Question

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are $1 \%, 2 \%$ and $3 \%$ respectively. The
maximum percentage error in the detection of the dissipated heat will be :

Accepted Answer

Given, $\frac{\Delta R}{R} 	imes 100=1 \%$
$
\frac{\Delta F}{F} 	imes 100=2 \% 	ext { and } \frac{\Delta t}{t} 	imes 100=3 \%
$
We know that, heat produced due to current flowing through a resistor $R$.
$

H =I^{2} R t $
$
\Rightarrow  \frac{\Delta H}{H} =\frac{2 \Delta I}{I}+\frac{\Delta R}{R}+\frac{\Delta t}{t}$
$
\Rightarrow  \frac{\Delta H}{H} 	imes 100 =2\left(\frac{\Delta I}{I} 	imes 100ight)+\frac{\Delta R}{R} 	imes 100+\frac{\Delta t}{t} 	imes 100$
$
=2 	imes 2 \%+1 \%+3 \%=8 \%

$

Answer

2

Answer

4

Answer

6

Answer

8

Units , Dimensions and Error Analysis

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit are 1 \%, 2 \% and 3 \% respectively. The maximum percentage error in the detection of the dissipated heat will be :

Choose the correct answer: