the equivalentresistance of seri3s combination of two resistor is 9 ohm and that of parallel combination is 2 ohm. find thw resistance of resistor
Answers
Answer:
6 Ω , 3 Ω
Explanation:
Given-----> Equivalent resistance of series combination of two resistor is 9Ω and that of parallel combination is 2Ω .
To find -----> Resistance of resistor
Solution------> Let , required resistance are R₁ and R₂ .
We , know that, equivalent resistance in series connection of two resistance R₁ and R₂ is
R = R₁ + R₂
ATQ, R = 9Ω , putting in above , we get,
=> 9 = R₁ + R₂
=> R₁ + R₂ = 9 .......................( 1 )
We , know that , eqivalent resistance in parallel connection of two resistance is
1 / R¹ = 1 / R₁ + 1 / R₂
ATQ, R¹ = 2Ω , putting it , we get,
=> 1 / 2 = 1 / R₁ + 1 / R₂
=> 1 / 2 = ( R₁ + R₂ ) / R₁ R₂
Putting , R₁ + R₂ = 9 , we get,
=> 1 / 2 = 9 / R₁ R₂
=> R₁ R₂ = 18 ........................( 2 )
By equation ( 1 ) , we get,
R₁ + R₂ = 9
=> R₂ = 9 - R₁
Putting R₂ = 9 - R₁ , in equation ( 2 ) , we get,
=> R₁ ( 9 - R₁ ) = 18
=> 9R₁ - R₁² = 18
=> R₁² - 9R₁ + 18 = 0
Now , by splitting the middle term , we get,
=> R₁² - ( 6 + 3 ) R₁ + 18 = 0
=> R₁² - 6R₁ - 3R₁ + 18 = 0
=> R₁ ( R₁ - 6 ) - 3 ( R₁ - 6 ) = 0
=> ( R₁ - 6 ) ( R₁ - 3 ) = 0
If , R₁ - 6 = 0
=> R₁ = 6 Ω
R₂ = 9 - R₁
= 9 - 6
R₂ = 3 Ω
If , R₁ - 3 = 0
=> R₁ = 3 Ω
R₂ = 9 - R₁
= 9 - 3
=> R₂ = 6 Ω
So answer is 6 Ω and 3 Ω .
Answer:
6 ohms and 3 ohms
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