Question

a uniform wire of resisitance r is cut into three equal pieces and those pieces are joined in parallel. what is the resistance of the combination

Answer 1

Let Total Resistance be R.

➵ Rs = R₁ + R₂ + R₃

Here it is necessory to mention that wire R is cut in 3 equal pieces. Therefore,

➵ R₁ = R₂ = R₃

➵ Rs = 3R₁

Now these three small parts are arranged in parallel combination.

➵ 1/R = 1/R₁ + 1/R₂ + 1/R₃

➵ 1/R = 3/R₁

➵ Rp = R₁/3

Dividing Rs by Rp we get,

➵ Rs/Rp = 3R₁ × 3/R₁

➵ Rs = 9Rp

Rs = 9 × Rp

Answer 2

Answer:Resistance of a wire is directly proportional to its length. Hence, a uniform wire of resistance R is cut into 3 smaller pieces, the resistance of each of the smaller wires would be R/3.  

 

When connected in parallel  

1/Req = 1/R1 + 1/R2 + 1/R3

1/Req = 3/R + 3/R + 3/R

1/Req = 9/R

Req = R/9