Question

28. Two resistors when connected in series, their effective resistance is 9 ohm. Their effective resistance become 2ohm when they are connected in parallel. Find the value of the resistors.​

Answer 1

Given: Two resistors when connected in series, their effective resistance is 9 ohm. Their effective resistance become 2ohm when they are connected in parallel.

Need to Find : Value of the Resistors

Let the value of resistors be x & y respectively

When these resistors connected in series the effective resistance is 9 ohm

↠ x + y = 9 ------------------(i)

Now,

when these resistors connected in parallel their effective resistance is 2 ohm

↠ 1/x + 1/y = 1/2

↠ x + y/xy = 1/2 -----------------(ii)

On substituting the equation (i) into equation (ii) we get

↠ 9/xy = 1/2

↠ 18 = xy

↠ 18/y = x ----------(iii)

Now, substituting equation (iii) in equation (i) we get

↠ 18/y + y = 9

↠ y² + 18 = 9y

↠ y² - 9y + 18 = 0

↠ y² - 6y - 3y + 18 = 0

↠ y ( y-6) + 3 ( y - 6 ) = 0

↠( y + 3) ( y-6) = 0

↠ y = -3 or y = 6

Since , resistance can't be negative .

So , y = 6

On substituting the value of y = 6 in equation (i) we get

↠ x + 6 = 9

↠ x = 9-6

↠ x = 3

• Hence, the value of the resistors are 3 & 6 ohm respectively .

Answer 2

Information provided with us༄

• Two resistors when connected in series, their effective resistance is 9 ohm.

• Their effective resistance become 2 ohm when they are connected in parallel.

What we have to calculate ༄

• The required value of the resistor

Assumption ༄

Consider the two resistance be

$\rm \: R_1$

and

$\rm{R_2}$

respectively

Now ༄

$\rm \implies{Series \: connection =R_s=R_1 + R_2 }$

Or

$\rm \implies{ 9=R_1 + R_2 }$

$\rm \implies{R_2 = 9 - R_1}$

$\rm \implies{Parallel \: connection = }$

$\rm \mapsto \: R_p = \dfrac{R_1 \: R_2}{R_1 \: R_2}$

$\rm \mapsto \: 2= \dfrac{R_1 \: (9 - R_1)}{9}$

$\rm \mapsto \: R_{1}^{ \: \: \: 2} + 9 \: R_1 - 18 = 0$

$\bf \implies \: R_1 = 6 \: \Omega$

So ༄

$\bf \implies \: R_2 = 9 - 6 = 3 \: \Omega$

Therefore༄

$\rm \longrightarrow The \: required \: value \: of \: the \: resistor \: are \: 6 \: \Omega \: and \: 3 \: \Omega$