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

Answer 1

Answer: (B)

$R_{1}+R_{2}=9$ and $\frac{R_{1} R_{2}}{R_{1}+R_{2}}=2$
$ \Rightarrow R_{1} R_{2}=18$
$R_{1}-R_{2}=\sqrt{\left(R_{1}+R_{2}\right)^{2}-4 R_{1} R_{2}}$
$=\sqrt{81-72}=3$
$R_{1}=6 \Omega, R_{2}=3 \Omega$