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

Answer

Total resistance,\(R=\frac{20}{19}\;\Omega\)
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Solution

Given: \({{R}}_{1}=2\;\Omega\) 
 \(\mathit{R}_2=4\;\Omega\) 
 \(\mathit{R}_3=5\;\Omega\) 
When the resistors are in parallel, 
 \(\frac{1}{R}=\frac{1}{{R}_{1}}+\frac{1}{{R}_{2}}+\frac{1}{{R}_{3}}\) 
 \(\frac{1}{R}=\frac12+\frac 1 4+\frac 1 5\) 
\(\frac{1}{R}=\frac{10+5+4}{20}\)
\(\frac{1}{R}=\frac{19}{20}\) 
Total resistance,\(R=\frac{20}{19}\;\Omega\)
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