Question

What resistance must be connected to a 15ohm resistance to provide an effective resistance of 6 ohm

Answer 1

Hi,

Here is your answer

Given:

Equivalent resistance(R)=6Ω

Resistance(R1)=15Ω

To Find:

Resistance(R2)

Solution:

The series is connected in parallel as the equivalent resistance is less than the individual resistance,

The equation for finding the total resistance is

$\frac{1}{R} =\frac{1}{R1} +\frac{1}{R2}$

$\frac{1}{R2} =\frac{1}{R} -\frac{1}{R1}$

Substitute the given datas in the above equation

We get,

$\frac{1}{R2} =\frac{1}{6} -\frac{1}{15}$

$\frac{1}{R2} =\frac{1}{10}$

Hence

R2=10Ω

Notes:

1. If a series is connected in parallel, total resistance is given by

$\frac{1}{R} =\frac{1}{R1} +\frac{1}{R2} +......+\frac{1}{Rn}$

2. If a series is connected in series, total resistance is given by

R=R1+R2+.......+Rn

Hope this helps you.