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

The correct option is C $4\Omega$, $2\Omega$

Let the two resistances be $R_1$ and $R_2$.

Equivalent resistance of series connection, $R_s=R_1+R_2$

$\therefore$ $R_1+R_2=6$ $⟹R_2=6-R_1$ ...........(1)

Equivalent resistance of parallel connection, $R_p=\frac{R_1{R}_2}{R_1+R_2}$

$\therefore$ $\frac{4}{3}=\frac{R_1(6-R_1)}{6}$ (using 1)

We get $R_1^2-6R_1+8=0$

Or $(R_1-4)(R_1-2)=0$ $⟹R_1=2\Omega$ or $4\Omega$

Let say, $R_1=4\Omega$

$⟹$ $R_2=6-4=2\Omega$