Question

A wire when connected to 220v mains supply has power dissipation P₁ . Now , the wire is cut into two equal pieces which are connected in parallel to the same supply power dissipation in this case is P₂ . Then P₂: P₁ is ​

Answer 1

Answer:

P₂ : P₁ = 4:1

Explanation:

Case I

Using the formula ,

P = v²/R__________(I)

where , R is resistance of wire , V is voltageacross wire and P is power dissipation in wire

and R = ρl/A ___________________(II)

From Eqs (I) and (II) , we haveP₁ = v² /ρl/A

or, Ρ₁ = v² A/ρl ______________(III)

Case II

Let R₂ be net resistance of half wire

R₂ = R×R /R + R = R/2

where, R is the resistance of half wire .

=> R₂ = ρ(l/2)/A×2 = ρl/4A

or, P₂ = v² /ρl × 4A

P₂ = v²/ρl • 4A ________(IV)

hence, From equs (III ) and (IV), We get

P₁ /P₂ = 1/4

P₂ /P₁ = 4/1

∴ P₂ : P₁ = 4:1 Answer .

Answer 2

Answer:

hope it helps u..............