Question

Two resistors $R_1=(4\pm 0.8)\Omega$ and $R_2=(4\pm 0.4)\Omega$ are connected in parallel. The equivalent resistance of their parallel combination will be :

• A. $(4\pm 0.4)\Omega$
• B. $(2\pm 0.4)\Omega$
• C. $(2\pm 0.3)\Omega$
• D. $(4\pm 0.3)\Omega$

Answer 1

Answer: (C)

$\frac{1}{R_{\text{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}$
$\frac{1}{R_{\text{eq}}}=\frac{1}{4}+\frac{1}{4}$
$\Rightarrow R_{\text{eq}}=2\Omega$
Also $\frac{\Delta R_{\text{eq}}}{R_{\text{eq }}^2}=\frac{\Delta R_1}{R_1^2}+\frac{\Delta R_2}{R_2^2}$
$\frac{\Delta R_{\text{eq}}}{4}=\frac{.8}{16}+\frac{.4}{16}=\frac{1.2}{16}$
$\underline{\underline{\Delta }}{R}_{\text{eq}}=0.3\Omega$
$R_{\text{eq}}=(2\pm 0.3)\Omega$