Two resistance are given as R _ 1 = ( 10 ± 0 . 5 ) Ω and R _ 2 = (...

For a parallel combination the equivalent resistance is

$\dfrac{1}{R} = \dfrac{1}{{R}_{1}} + \dfrac{1}{{R}_{2}} . . . ( i )$

A general expression for error can be written as $x \pm ∆ x$

Differentiating equation (i)

$\dfrac{dR}{{R}^{2}} = d{R}_{1}{R}_{1}^{2} + d{R}_{2}{R}_{2}^{2} . . . ( ii )$

The equivalent resistance with ${R}_{1} = 10Ω \text{ and } {R}_{2} = 15Ω$ is

$\dfrac{1}{R} = \dfrac{1}{10} + \dfrac{1}{15}$

$⇒ R = \dfrac{150}{25} = 6Ω$

Substituting the above value in equation (ii)

$dR = 36\left(\dfrac{0 . 5}{100} + \dfrac{0 . 5}{15 \times 15}\right) = 0 . 26$

$⇒ R = 6 \pm 0 . 26$

Hence, the percentage error is

$\dfrac{dR}{R} \times 100 = \dfrac{0 . 26}{6} \times 100$$= 4 . 33$