Question

Two resistances $60.36\Omega$ and $30.09\Omega$ are connected in parallel. The equivalent resistance is

• A. $20\pm 0.08\Omega$
• B. $20\pm 0.06\Omega$
• C. $20\pm 0.03\Omega$
• D. $20\pm 0.10\Omega$

Answer 1

Answer: (A)

Equivalent resistance is
$R_{\text{parallel }}=\frac{R_1{R}_2}{R_1+R_2}=\frac{60\times 30}{60+30}=20\Omega$
and tolerance value is
$\Rightarrow \Delta R_P=R_P\left\{\frac{\Delta R_1}{R_1}+\frac{\Delta R_2}{R_2}-\frac{\Delta R_1+\Delta R_2}{R_1+R_2}\right\}$
$=20\left\{\frac{0.36}{60}+\frac{0.09}{30}-\frac{0.36+0.09}{90}\right\}$
$=20\{0.006+0.003-0.005\}=0.085\Omega$
So, resistance in parallel is $R_P=20\pm 0.08$