Question

The equivalent resistance of parallel combination is:

• A. Lower than the value of lowest resistance in the combination
• B. Higher than the value of lowest resistance in the combination
• C. Both A and B
• D. None of these

Answer 1

The correct option is A Lower than the value of lowest resistance in the combination

Consider two resistors having resistances $R_1$ and $R_2$.

The equivalent resistance of $R_1$ and $R_2$ in parallel is,

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$

$⟹R_{eq}=\frac{R_1{R}_2}{R_1+R_2}$

For any values of $R_1$ and $R_2$, $R_{eq}$ will be less than $R_1$ and $R_2$.

For example,

Let $R_1=2\Omega$

$R_2=6\Omega$

Then,

Equivalent resistance of $R_1$ and $R_2$ in parallel,

$R_{eq}=\frac{R_1{R}_2}{R_1+R_2}$

$R_{eq}=\frac{2\times 6}{2+8}$

$R_{eq}=\frac{12}{8}$

$R_{eq}=1.5\Omega$

$⟹R_{eq}<R_1\text{and}{R}_{eq}<R_2$