Question

TWO WIRES A AND B OF SAME MATERIAL HAVING SAME LENGTH ,HAVING CROSS SECTIONAL AREA IN THE RATIO 1:4,WHAT WOULD BE THE RATIO OF HEAT PRODUCED IN THESE WIRES ?

Answer 1

we know that,
Heat α 1/area
let area of wire a be A and that of b be 4A.
RATIO OF HEAT OF WIRE A TO B= 1/A/1/4A
=4/1=4:1

Answer 2

The ratio of heat produced by wire A to wire B is 4:1.

Explanation:

The heat produced in a wire is given by :

$H=I^2Rt$

R is resistance, $R=\rho \dfrac{l}{A}$

So,

$H=I^2\dfrac{\rho l}{A}t$

So, it is clear that the heat produced is inversely proportional to area of cross section. So,

$H=\dfrac{1}{A}$

For wire A,$H_A=\dfrac{1}{A_A}$  .......(1)

For wore B, $H_B=\dfrac{1}{A_B}$ ..........(2)

Dividing equation (1) and (2) we get :

$\dfrac{H_A}{H_B}=\dfrac{A_B}{A_A}$

Given : $\dfrac{A_A}{A_B}=\dfrac{1}{4}$

$\dfrac{H_A}{H_B}=\dfrac{4}{1}$

So, the ratio of heat produced by wire A to wire B is 4:1.

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