Question

If three resistors of resistance $ 2\,\Omega ,\,4\,\Omega$ and $ 5\,\Omega$ are connected in parallel then the total resistance of the combination will be:

• A. $ \frac{20}{19}\Omega $
• B. $ \frac{19}{20}\Omega $
• C. $ \frac{19}{10}\Omega $
• D. $ \frac{10}{19}\Omega $

Answer 1

Answer: (A)

Here : Resistance of the Ist resistors $R_{1}=2\, \Omega$
Resistance of the IInd resistor $R_{2}=4\, \Omega$
Resistance of the IIIrd resistor $R_{3}=5\, \Omega$
The relation for the equivalent resistance
$R_{e q}$ of the circuit in parallel combination
$\frac{1}{R_{e q}} =\frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}$
$=\frac{1}{2}+\frac{1}{4}+\frac{1}{5}=\frac{19}{20}$
$R_{e q} =\frac{20}{19} \Omega$