Question

What resistance must be connected to a $15\Omega$ resistance to provide an effective resistance of $6\Omega$?

• A. $15\Omega$
• B. $10\Omega$
• C. $5\Omega$
• D. $2\Omega$

Answer 1

The correct option is B

$10\Omega$

Given resistance, $R_1=15\Omega$

Effective resistance, $R=6\Omega$

Let the resistance to be connected be $R_2$.

In a parallel combination of resistors, the equivalent resistance is less than the individual resistors in the circuit.

Since effective resistance is less than $R_1$, so $R_2$ must be connected in parallel with $R_1$.

In parallel combination, effective resistance,
$\frac{1}{R}=\frac{1}{R_1}+\frac{1}{R_2}$
$\Rightarrow \frac{1}{6\Omega }=\frac{1}{15\Omega }+\frac{1}{R_2}$
$\Rightarrow \frac{1}{R_2}=\frac{1}{6\Omega }-\frac{1}{15\Omega }$
$\Rightarrow \frac{1}{R_2}=\frac{15-6}{15\times 6\Omega }$
$\Rightarrow R_2=\frac{90\Omega }{9}$

Hence, $R_2=10\Omega$