Question

if three resistance 2ohm, 3ohm, 5ohm when they are connected in parllel the equivalent resistance of three resistanceis​

Answer 1

As we know,

The formula for parallel resistance is:-

$\large \frak \red{ \frac{1}{r} } = \tt\frac{1}{r} + \frac{1}{r} + \frac{1}{r}$

So,

$\tt \: \frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } + \frac{ 1 }{ 5 }$

• Least common multiple of 2 and 3 is 6.Convert $\tt\frac{1}{2} \: and \: \frac{1}{3}$ to fractions with denominator 6.

$\tt\frac{3}{6}+\frac{2}{6}+\frac{1}{5}$

• Since $\tt\frac{3}{6} and \frac{2}{6}$ have the same denominator, add them by adding their numerators.

$\tt\frac{3+2}{6}+\frac{1}{5} \\ \\ \tt\frac{5}{6}+\frac{1}{5}$

• Least common multiple of 6 and 5 is 30. Convert $\tt \: \frac{5}{6} and \frac{1}{5}$to fractions with denominator 30.

$\tt\frac{25}{30}+\frac{6}{30} \\ \\ \tt\frac{25+6}{30} \\ \\ \tt\frac{31}{30}\approx 1.033333333 \\ \\ \large \frak \red{resistance = 1.033 ohm}$

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Answer 2

As we know,

$\tt\purple{ \frac{1}{r_0} } = \tt\frac{1}{r_1} + \frac{1}{r}_2 + \frac{1}{r_3}$

So,

$⇉ \tt \frac{ 1 }{ 2 } + \frac{ 1 }{ 3 } + \frac{ 1 }{ 5 }$

$⇉ \tt\frac{3}{6}+\frac{2}{6}+\frac{1}{5}$

$⇉\tt\frac{3+2}{6}+\frac{1}{5}$

$⇉\tt\frac{5}{6}+\frac{1}{5}$

$⇉\tt\frac{25}{30}+\frac{6}{30}$

$⇉\tt\frac{25+6}{30}$

$⇉\tt\frac{31}{30}\approx 1.033333333$

$\large \frak \purple{resistance = 1.033 ohm}$