Question

if resistors of 10ohm,15ohm,25ohm and xohm are connected in parallel in circuit and total resistance is 20ohm ,then find the value of x​

Answer 1

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Answer:

$let \: \frac{1}{ R_{p} } \: is \: the \: total \: resistance \: of \: circuit. \\ R_{1} = 10 \: ohm \\ R_{2} = 15 \: ohm \\ R_{3} = 25 \: ohm \\ R_{4} = x \: ohm$

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$\frac{1}{ R_{p}} = \frac{1}{ R_{1}} + \frac{1}{R_{2}} + \frac{1}{ R_{3}} + \frac{1}{ R_{4} } \\ \\ \frac{1}{20} = \frac{1}{10} + \frac{1}{15} + \frac{1}{25} + \frac{1}{x} \\ \\ \frac{1}{x} = \frac{1}{20} - \frac{1}{10} - \frac{1}{15} - \frac{1}{25} \\ \\ \frac{1}{x} = \frac{10 - 20}{200} - ( \frac{25 + 15}{375} ) \\ \\ \frac{1}{x} = \frac{ - 10}{200} - \frac{40}{375} \\ \\ \frac{1}{x} = \frac{ - 3750 - 8000}{75000} \\ \\ \frac{1}{x} = \frac{11750}{75000} \\ \\ x= \frac{75000}{11750} \\ \\ x = 6.382 \: ohm \:$

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