Question

heating coils, one of fine wire and other of thick wire made of same material and lengths are connected one by one to a source of electricity. Which coil produce heat at greater rate? Justify.​

Answer 1

Answer:

Given,

2 heating coils of same length, l

Let resistance of thin wire be R

1

resistance of thick wire be R

2

We know,

for same material, resistivity ρ is same

Cross section area of thin wire = A

1

Cross section area of thick wire = A

2

A

2

>A

1

R=

A

ρl

⟹Rα

A

1

⟹R

1

>R

2

(∵A

2)

>A

1)

Rate of heat generation, P=

R

V

2

Both are connected to the same source V

Pα

R

1

⟹P

2

>P

1

(∵R

1

>R

2)

A thick wire coil will produce heat at a rate of heat generation, P=

R

V

2

Both are connected to the same source V

Pα

R

1

P

1

= Rate of heat generation by thin wire

P

2

= Rate of heat generation by thick wire

R

1

>R

2

⟹P

2

>P

1

The thick wire coil will generate heat at a greater rate.

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Answer 2

Given,

2 heating coils of same length, l

Let resistance of thin wire be R1​

resistance of thick wire be R2​

We know,

for same material, resistivity ρ is same

Cross section area of thin wire = A1​

Cross section area of thick wire = A2​

A2​>A1​

R=ρl​/A⟹Rα1​/A

⟹R1​>R2​ (∵A2​>A1​)

Rate of heat generation, P=V​/R

Both are connected to the same source V

PαR1​

⟹P2​>P1​ (∵R1​>R2​)

A thick wire coil will produce heat at a rate of heat generation, P=V​ ² /R

Both are connected to the same source V

Pα1​/R

P1​ = Rate of heat generation by thin wire

P2​ = Rate of heat generation by thick wire

R1​>R2​

⟹P2​>P1​

The thick wire coil will generate heat at a greater rate.

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