Question

What resistance must be connected in parallel to a $4\Omega$ resistance to make the effective resistance equal to $2.4\Omega$?

• A. $6\Omega$
• B. $7\Omega$
• C. $5\Omega$
• D. $3\Omega$

Answer 1

The correct option is A $6\Omega$

Given:
Value of resistance, $R_1$ = $4\Omega$
Equivalent resistance to be obtained, $R_{eq}$ = $2.4\Omega$
Let the new resiatance be $R_2$.
For a parallel combination of resistors,
$R_{eq}=\frac{R_1\times R_2}{R_1+R_2}$
$⟹2.4=\frac{R_2\times 4}{4+R_2}$
$⟹9.6+2.4R_2=4R_2$
$\Rightarrow R_2=\frac{9.6}{1.6}=6\Omega$
So, to make an equivalent of $2.4\Omega$, a resistance of $6\Omega$ needs to be connected in parallel to the given resistance.