Question

Two resistances $R_1$ and $R_2$ give a combined resistance of 4.5 $\Omega$ when in series and 1 $\Omega$ when in parallel. The value of resistances are

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

Answer 1

The correct option is C

1.5 Ω, 3 Ω

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

4.5 = $R_1$ + $R_2$

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

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

$R_1$= $\frac{4.5}{R_2}$

Substituting and solving we get,

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