Question

Masses of three wires of same material are in the ratio .1:3:5 and their lengths are in the ratio 5:3:1. if they are connected in series with a battery then the ratio of heats produced in them will be

Answer 1

The ratio of heats produced in the material is H1  : H 2   : H 3  = 125 : 15 : 1

Explanation:

The resistance of wire is given by: R = ρl /A

But, A = ml/d

where m is mass, l is length and d is the density of material of conductor.

Hence, R = ρl ÷ m/dl =  ρd l^2 / m

R ∝   l^2 / m

Let, R  1 , R2  and R 3  be the resistances of three wires, l 1 , l 2  and l 3 be the lengths of three wires and m1, m2 and m 3  be the masses of three wires. Therefore,

R1   ∝  l1^2/m1

​R1 2 ∝  l2^2/m2

R3   ∝  l3^2/m3

Also, heat produced in the wire is: H = I^2 R

current through them is same. Therefore,

H 1  ∝R  1

​H 12 ∝R  2

H 3  ∝R  13

The ratio of heats:

H1  : H 2   : H 3  =(  l1^2/m1   ):( l 2^ 2/  m 2    ):(    l3^ 2/m3 )

H1  : H 2   : H 3  = ( 5^2/1 ) : (3^2/ 3) : (1^2 /5)

H1  : H 2   : H 3  = (25/1) : (9/3) : (1/5)

H1  : H 2   : H 3  = 125 : 15 : 1

Thus the ratio of heats produced in the material is H1  : H 2   : H 3  = 125 : 15 : 1

​Also learn more

What is young modulus and elasticity. ?

https://brainly.in/question/6086284