Question

The equivalent resistance of two resistors connected in series is $6\Omega$ and their parallel equivalent resistance is $\frac{4}{3}\Omega$. What are the values of resistances ?

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

Answer 1

Answer: (C)

Let the value of resistance be $R_1$ and $R_2$ respectively.
When $R_1$ and $R_2$ resistances are in series
So, $R_1+R_2=6\Omega \dots (i)$
(According to the question)
When $R_1$ and $R_2$ resistances are in parallel
So, $\frac{R_1{R}_2}{R_1+R_2}=\frac{4}{3}\Omega \dots (ii)$
From the Eq. (i), we get
$\frac{R_1{R}_2}{6}=\frac{4}{3}$
$R_1{R}_2=4\times 2$
$R_1{R}_2=8\dots (iii)$
We know that
$R_1-R_2=\sqrt{{\left(R_1+R_2\right)}^2-4R_1{R}_2}$
$=\sqrt{36-4\times 8}$
$R_1-R_2=\sqrt{4}$
$R_1-R_2=2\Omega \dots (iv)$
From the Eqs. (i) and (iv), we get
$R_1=4\Omega ,R_2=2\Omega$