Two resistors are connected (i) in series (ii) in parallel. The equivalent resistance in the two cases are 9 ohm and 2 ohm respectively. Then the resistances of the component resistors are

Question

Two resistors are connected (i) in series (ii) in parallel. The equivalent resistance in the two cases are 9 ohm and 2 ohm respectively. Then the resistances of the component resistors are (A) 2 ohm and 7 ohm (B) 3 ohm and 6 ohm (C) 3 ohm and 9 ohm (D) 5 ohm and 4 ohm

Tardigrade Admin · Accepted Answer

R1+R2=9 and (R1 R2/R1+R2)=2 ⇒ R1 R2=18 R1-R2=√(R1+R2)2-4 R1 R2 =√81-72=3 R1=6 Ω, R2=3 Ω

Q. Two resistors are connected (i) in series (ii) in parallel. The equivalent resistance in the two cases are $9 o hm$ and 2 ohm respectively. Then the resistances of the component resistors are

2 ohm and 7 ohm

3 ohm and 6 ohm

3 ohm and 9 ohm

5 ohm and 4 ohm

$R_{1} + R_{2} = 9$ and $\frac{R _{1} R _{2}}{R _{1} + R _{2}} = 2$
$\Rightarrow R_{1} R_{2} = 18$
$R_{1} - R_{2} = (R_{1} + R_{2})^{2} - 4 R_{1} R_{2}$
$= 81 - 72 = 3$
$R_{1} = 6Ω, R_{2} = 3Ω$

Q. Two resistors are connected (i) in series (ii) in parallel. The equivalent resistance in the two cases are 9ohm and 2 ohm respectively. Then the resistances of the component resistors are