Question

Two resistors are connected (1) in series (2) 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)

3$ohm$ and 6$ohm$

Answer 2

$R_{1} + R_{2} = 9$ and $\frac{R_{1}R_{2}}{R_{1} + R_{2}} = 2$ ⇒ $R_{1}R_{2} = 18$

$R_{1} - R_{2} = \sqrt{(R_{1} + R_{2})^{2} - 4R_{1}R_{2}} = \sqrt{81 - 72} = 3$

$R_{1} = 6\Omega,R_{2} = 3\Omega$