Question

Calculate the effect the resistance when two resistors of resistances 10 $\Omega$ and 20 $\Omega$ are connected in parallel.

• A. 0.15 $\Omega$
• B. 6.66 $\Omega$
• C. 3.33 $\Omega$
• D. 0.25 $\Omega$

Answer 1

The correct option is B 6.66 $\Omega$

We know that in parallel connection of resistors $R_1,R_2,R_3...R_n$ the equivalent resistance is given by-

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}+\frac{1}{R_3}+...+\frac{1}{R_n}$

For two given resistances-

$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$

$⟹R=\frac{R_1{R}_2}{R_1+R_2}$

$⟹R=\frac{10\times 20}{10+20}=\frac{200}{30}$

$⟹R=6.66\Omega$

Answer-(B)