Question

the effective resistance of two resistors is 9 ohm in series and 14/9 ohm in parallel. find the value of each resistors​

Answer 1

Answer :

• Value of resistors will be 2 Ω and 7 Ω

Explanation :

Given that,

• effective resistance of two resistors connected in series is 9 Ω
• effective resistance when connected in parallel is 14/9 Ω

we need to find,

• Value of each resistor

So,

Let, values of two resistors be R₁ and R₂

then,

→ Effective resistance in series = 9

→ R₁ + R₂ = 9   ______ equation (1)

And,

→ Effective resistance in parallel = 14/9

→ 1/R₁  +  1/R₂ = 1/(14/9)

→ ( R₂ + R₁ ) / (R₁ R₂) = 9 / 14

[ using equation (1) ]

→ ( 9 ) / (R₁ R₂) = 9 / 14

→ R₁ R₂ = 14

[ using equation (1) we can write (R₂ = 9 - R₁) ]

→ R₁ ( 9 - R₁ ) = 14

→ 9 R₁ - R₁² = 14

→ R₁² - 9 R₁ + 14 = 0

[ writing R₁ = x ]

→ x² - 9 x + 14 = 0

[ solving quadratic equation ]

→ x² - 7 x - 2 x + 14 = 0

→ x ( x - 7 ) - 2 ( x - 7 ) = 0

→ ( x - 2 ) ( x - 7 ) = 0

→ x = 2  or x  =  7

so,

Taking x = R₁ = 2 Ω and putting in equation (1) we will get R₂ = 7 Ω

and taking x = R₂ = 7 Ω and putting in equation (1) we will get R₂ = 2 Ω.

Therefore,

• Value of resistors will be 2 Ω and 7 Ω .