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(a) Three resistors 2 Ω, 4 Ω and 5 Ω are combined in parallel. What is the total resistance of the combination?

3.4  (a) Three resistors 2 Ω, 4 Ω and 5 Ω are combined in parallel. What is the total resistance of the combination?

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We know that when resistances are in parallel combination, the total resistance R is given by:

\frac{1}{R} = \sum \frac{1}{R_{i}}

Therefore, Total resistance of the given three resistances in parallel combination is

\frac{1}{R} = \frac{1}{R_{1}}+\frac{1}{R_{2}}+\frac{1}{R_{3}}

\implies \frac{1}{R} = \frac{1}{2}+\frac{1}{4}+\frac{1}{5} = \frac{10+5+4}{20}=\frac{19}{20}

\implies R= \frac{20}{19} = 1.05 \Omega

Hence, the total resistance is 1.05 \Omega

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