Question

Find out the equivalent resistance between the points A and B in the given diagram. ​

Answer 1

Solution :-

As per the given data ,

• R 1 = 1 Ω

• R 2 = 6 Ω

• R 3 = 3 Ω

• R 4 = R 5 = R 6 = R =2 Ω

R 2 and R 3  are connected in parallel combination ,

Equivalent resistance of n no of resistors connected in parallel combination is given by ,

1 / Rp = 1 / R 1 + 1 / R 2 + ... + 1 / Rp

Hence ,

➜ 1 / Rp = 1 / R 2 + 1 / R 3

➜ 1 / Rp = 1 / 6 + 1 / 3

➜ 1 / Rp = 1 + 2 / 6

➜ 1 / Rp = 3 / 6

➜ 1 / Rp = 1 / 2

➜ Rp = 2 Ω

Three resistors each having resistance of 2 Ω are connected in parallel combination .

➜ 1 / Rp ' = 1 / R + 1 / R + 1 / R

➜ 1 / Rp ' = 3 / R

➜ Rp ' = 2 / 3  Ω

Now Rp and Rp ' are connected in parallel with each other

➜ 1 / Rp " = 1 / Rp + 1 / Rp '

➜ 1 / Rp " = 1 / 2 + 3 / 2

➜ 1 / Rp " = 4 / 2

➜ 1 / Rp " = 2

➜ Rp " = 1/ 2  Ω

Now ,

Rp " and R 1 are connected in series combination ,

Equivalent resistance of n no of resistors connected in series  combination is given by ,

➜ Rs = R 1 + R 2 ... + Rn

Hence ,

➜ Rs = Rp " + R1

➜ Rs = 1/2 + 1

➜ Rs = 3 / 2

➜ Rs = 1.5 Ω

The equivalent resistance of the combination is 1.5 Ω