Question

R1 = (15 ± 0.5) Ω
R2 = (10 ± 0.5) Ω
Find % error in equivalent resistance if resistors R1 and R2 are connected in parallel ?

• A. 5%
• B. 4.33%
• C. 3%
• D. 3.33%

Answer 1

Answer: (B)

4.33%

Answer 2

$\frac{1}{R_{eq}}=\frac{1}{R_{1}}+\frac{1}{R_{2}}$ and $R_{eq}=\frac{150}{25}=6\Omega$
$\frac{dR_{eq}}{R^{2}_{eq}}=\frac{dR_{1}}{R^{2}_{1}}+\frac{dR_{2}}{R^{2}_{2}}$
$\frac{dR_{eq}}{R_{eq}}=R_{eq}[\frac{dR_{1}}{R^{2}_{1}}+\frac{dR_{2}}{R^{2}_{2}}]$
$\frac{dR_{eq}}{R_{eq}}=6[\frac{0.5}{15^{2}}+\frac{0.5}{10^{2}}]$
Therefore, $$% \frac{dR_{eq}}{R_{eq}}=6\times0.5\times 100[\frac{1}{225}+\frac{1}{100}]$$=6\times0.5\times 100\times \frac{325}{225\times 100}=4.33%
So, the answer is (B): 4.33%$$