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 $R_{P}=20 \pm 0.08$