Question

find the equivalent resistance with explanation plz​

Answer 1

Given :

• R₁ = R₂ = 6 Ω
• R₃ = 3 Ω
• R₄=8 Ω
• R₅ = R₆ = 10Ω
• R₇ = 5 Ω

Please refer to the attachment first !!!

Solution :

Step I: Use the potential method in order to write the potential difference across each resistor.

Step II: Rearrange the circuit

Step III:

Left side :

R₅ and R₆ are in parallel

⇒ 1 / Rp = 1 / 10 + 1 / 10

⇒ 1 / Rp = 2 / 10

⇒ Rp = 5

⇒ R₇ = 5 Ω

Hence,

⇒ Rp / R₇ = 5 / 5 = 1 / 1  .... (1)

Right side :

R₁ and R₂ are parallel to each other.

⇒ 1 / Rp' = 1 / R₁ + 1 / R₂

⇒ 1 / Rp' = 1 / 6 + 1 / 6

⇒ 1 / Rp' = 2 / 6

⇒ Rp' = 3 Ω

⇒ R₃ = 3 Ω

Hence,

⇒ Rp' / R₃ = 3 / 3 = 1 ... (2)

⇒ Rp / R₇ = Rp' / R₃

Hence, a Wheatstone bridge is formed.

So we can neglect the 8 Ω resistor as no current is flowing through it.

________________________

Now,

Rp and R₃ are connected in series with each other

⇒ Rs = Rp + R₃

⇒ Rs = 5 + 3

⇒ Rs = 8Ω  

Rp' and R₇ are connected in series with each other.

⇒ Rs' = Rp' + R₇

⇒ Rs' = 5 + 3

⇒ Rs' = 8 Ω

Rs' and Rs are parallel to each other.

⇒ 1 / R = 1 / Rs + 1 / Rs'

⇒ 1 / R = 1 / 8 + 1 / 8

⇒ 1 / R = 2 / 8

⇒ R = 4 Ω  

Answer 2

hope so it is helpful.....!!