Question

Two resistors are connected a) in series b) in parallel.
The equivalent resistance in two cases are $9\Omega$ and $2\Omega$ respectively. Then the resistance of the component resistors are.

• A. $2\Omega$ and $7\Omega$
• B. $3\Omega$ and $6\Omega$
• C. $3\Omega$ and $9\Omega$
• D. $5\Omega$ and $4\Omega$

Answer 1

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

$\text{Step 1: Equivalent resistance for series connection}$

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

$R_s=R_1+R_2$

$\Rightarrow$ $9=R_1+R_2$

$\Rightarrow R_1=9-R_2$ $......\left(1\right)$

$\text{Step 2: Equivalent resistance for parallel connection}$

$R_p=\frac{R_1{R}_2}{R_1+R_2}$

$\Rightarrow$ $2=\frac{R_1{R}_2}{R_1+R_2}$ $......\left(2\right)$

$\text{Step 3: Solving Equations}$

Put the value of $R_1$ from $\left(1\right)$ in equation $\left(2\right)$

$2=\frac{(9-R_2)R_2}{9}$

$\Rightarrow R_2^2-9R_2+18=0$

$\Rightarrow (R_2-6)(R_2-3)=0$

$\Rightarrow R_2=6\Omega$ or $R_2=3\Omega$

From equation (1)

$\Rightarrow R_1=3\Omega$ or $R_1=6\Omega$

Hence, option(B) is correct.