Question

for a given current and resistance what is the change in the heat produced in a conductor if the time for which current flows through a conductor is tripled, one third time of the original? Class 10 CBSE

Answer 1

Given:

Current flowing through a conductor is tripled and the time period is made one-third. The resistance value is specified.

To find:

Change in heat production by the wire.

Calculation:

For given resistance , current and time , the heat produced by any wire is given by:

$\boxed{ \sf{H = {I}^{2} \times R \times t}}$

I is the current , R is the resistance and t is the time.

Now , new current is 3I and new time of observation is t/3.

Let new heat be $H_{2}$

$\sf{ \therefore \: H_{2} ={(3I)}^{2} \times R \times ( \dfrac{t}{3} )}$

$\sf{ = > \: H_{2} =( \cancel{9} \: {I}^{2}) \times R \times ( \dfrac{t}{ \cancel{3}} )}$

$\sf{ = > \: H_{2} =3{I}^{2}\times R \times \: t}$

$\sf{ = > \: H_{2} =3H}$

So , change in heat produced be :

∆Heat = 3H - H = 2H

So final answer is:

Change in Heat produced will be twice the initial heat.

Answer 2

2/3 of the original heat is reduced if time is 1/3rd of original time

Explanation:

Heat produced in conductor = I²Rt

I = Current flowing through conductor  

R = Resistance of conductor

t = time of current flow

original time = t

original heat  H

H =  I²Rt

time for which current flows now = t/3

New Heat  =  I²R(t/3)  = H/3

Change in heat   =   H - H/3  = 2H/3

Change in heat produced = (2H/3)/H = 2/3

Change in heat produced = 2/3 of the original heat is reduced

if Current is tripled & time is one thirs

Then New Heat

= (3I)²R(t/3)

= 3H

Change in heat = 3H - H = 2H

Change in heat produced = Twice the original heat is increased

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