Question

three resistors of 6 ohm 3 ohm and 2 ohm are connected together so that the total resistance is greater than 6 ohm but less than 8 home draw a diagram to show this arrangement and calculate the total resistance

Answer 1

Here, in 3ohms and 2ohms are in parallel combination,
I.e. 1/R = 1/3+1/2 =2+3/6 =5/6
therefore ,1/R = 5/6
R=6/5
Now, in series, R= 6/5+ 6= 6+ 30/5=36/5=7.2ohms
therefore , total resistance R =7.2ohms

Answer 2

Given:

• Three resistances 6 ohm, 3ohm, 2 ohm is given.

To find:

• Arrangement in which net resistance will be more than 6 ohm and less than 8 ohm.

Calculation:

First of all, let's put 2ohm and 3 ohm in parallel.

The equivalent resistance will be :

$\dfrac{1}{R} = \dfrac{1}{2} + \dfrac{1}{3}$

$\implies \dfrac{1}{R} = \dfrac{2 + 3}{6}$

$\implies \dfrac{1}{R} = \dfrac{5}{6}$

$\implies R = \dfrac{6}{5} \: ohm$

Now, put this combination in series with 6 ohm.

So, net resistance will be :

$R_{net} = \dfrac{6}{5} + 6$

$\implies R_{net} = 1.2 + 6$

$\implies R_{net} =7.2 \: ohm$

$\implies 6 \: ohm < R_{net} < 8 \: ohm$

Hope It Helps