Question

find out the equivalent resistance with step by step process ​

Answer 1

Solution:-

(1)

Here ,

• R 1 =R 2 =R 3 = R4 =  1 Ω

Here , R 3 and R 4 each having resistance of 1 Ω are connected in parallel with each other

Equivalent resistance when resistors are connected in parallel is given by the formula ,

⟹ 1 / Rp = 1 / R 3 + 1 / R 4

⟹ 1 / Rp = 1 / 1 + 1 / 1

⟹ 1 / Rp = 2 / 1

⟹  Rp = 0.5  Ω

Now R 1 ,R 2 and Rp are connected in series with each other

Equivalent resistance when resistors are connected in series is given by the formula ,

⟹ Rs = Rp + R1 + R2

⟹ Rs = 0.5 + 1 + 1

⟹ Rs = 2.5  Ω

Net equivalent resistance = 2.5  Ω

____________

(2)

Here ,

• R 1 = 1  Ω

• R 2 = 3  Ω

• R 3 = 4  Ω

Here R 1 and R 2 are connected in series with each other

⟹ Rs = 1 + 3

⟹ Rs = 4 Ω

Now R s and R 3 are connected in parallel

⟹  1 / Rp = 1 / R 3 + 1 / R s

⟹  1 / Rp = 1 / 4 + 1 / 4

⟹  1 / Rp = 2 / 4

⟹ 1 / Rp = 1 / 2

⟹ Rp = 2 Ω

Net equivalent resistance = 2  Ω

____________

(3)

Here ,

• R1 = 2 Ω

• R2 = 8 Ω  

• R3 = 6 Ω  

• R4 = 3 Ω  

Here , R2 and R3 are connected in parallel to each other

⟹ 1 / Rp = 1 / R 2 + 1 / R 3

⟹  1 / Rp = 1 / 8 + 1 / 6

⟹1 / Rp = 3 + 4/ 24

⟹  1 / Rp = 7 / 24

⟹ Rp = 24 / 7

⟹ Rp = 3.42 Ω

Now R1 ,Rp  and R 4 are connected in series with each other

⟹ Rs = R 1 + Rp + R 4

⟹ Rs = 2+ 3.42 + 3

⟹ Rs = 8.42  Ω

Net equivalent resistance = 8.42  Ω