Question

Three resistance of 4 ohms,6 ohms,12 ohms are given .How will they be joined to get a resistance of 8 ohms .Show the line of reasoning.

Answer 1

Three resistors of resistance 4 ohm, 6 ohm and 12 ohm are given.

We have to connect all the three resistors in such a way that their resistant is 8 ohm.

Let's denote the 4 ohm resistor by R1, 6 ohm resistor by R2 and 12 ohm resistor by R3.

Firstly connect R2 and R3 in parallel.

For parallel combination:

---------------| R2 |---------------

---------------| R3 |---------------

1/Rp = 1/R2 + 1/R3

Substitute the known values,

1/Rp = 1/6 + 1/12

1/Rp = 1/6(1/1 + 1/2)

1/Rp = 1/6(3/2)

1/Rp = 1/4

Rp = 4 ohm

Now, connect the R1 and Rp in series.

For series combination:

------------| R1 |--------| Rp |-------------

Rs = R1 + Rp

Substitute the values,

Rs = 4 + 4

Rs = 8 ohm

Therefore, the 6 ohm and 12 ohm resistors are connected in parallel and their resultant is connected in series with 4 ohm resistor.