Question

Two resistances $R_1$ and $R_2$ give an equivalent resistance of 4.5 $\Omega$ when connected in series and 1 $\Omega$ when connected in parallel. Then the value of resistances are___________.​

• A. 3 , 6
• B. 3 , 9
• C. 1.5 , 3
• D. 1.5 , 0.5

Answer 1

The correct option is C

1.5 , 3

For series combination, $R_{eq}$= $R_1$ + $R_2$

4.5 = $R_1$ + $R_2$ (Given) ......... (i)

For parallel combination, $R_{eq}=\frac{R_1{R}_2}{R_1+R_2}$

1 = $\frac{R_1{R}_2}{4.5}$

or, $R_1{R}_2=4.5$

$R_1$= $\frac{4.5}{R_2}$ ......... (ii)

Put the value of $R_1$ in eqn. (i).

Substituting and solving we get,

$R_1$= 1.5 $\Omega$, $R_2$= 3 $\Omega$