Question

The resultant resistance of two resistors when connected in series is 9 ohm. When they are connected in parallel, the resistance is 2 ohm.The resistances of these resistors are:

• A. 7$\Omega$,2$\Omega$
• B. 6$\Omega$, 3$\Omega$
• C. 5$\Omega$,4$\Omega$
• D. 8$\Omega$,1$\Omega$

Answer 1

The correct option is B 6$\Omega$, 3$\Omega$

$R_1+R_2=9\Omega$
$\frac{R_1{R}_2}{R_1+R_2}=2$
$\Rightarrow R_1{R}_2=18$
$\Rightarrow R_1+\frac{18}{R_1}=9$
$R_1^2-9R_1+18=0$
$(R_1-6)(R_1-3)=0$
$\Rightarrow R_1=6\Omega ;R_2=3\Omega$