Question

current through a metallic conductor is doubled while its resistance and the time are held constants. Under these conditions, the heat generated in the conductor will increase by a factor of - (2) Two (b) Four (c) Six (d) Eight

(mcq) plz help me out​

Answer 1

Answer:

b) four

bcz het produced is directly proportional to current squared

Answer 2

Given : Current through a metallic conductor is doubled while its resistance and the time are held constants.

To Find : Factor at which heat generated in the conductor will increased is.

Solution :

The heat produced in conducting wire is given by joules law as :

$\[H = {I^2}Rt\]$

Where,

H = Heat produced in conducting wire.

I = Current through conductor.

R = Resistance of conductor.

t = Time of current flow.

Thus from that equation, for current :  

The amount of heat produced in current conducting wire, is proportional to the square of the amount of current that is flowing through the circuit, when the electrical resistance of the wire and the time of current flow is constant.

        $\[H \propto {I^2}\]$ (when R, t are constant).

Thus  $\[\frac{{{H_1}}}{{{I_1}^2}} = cons\tan t\]$    

Here,  $\[\frac{{{H_1}}}{{{I_1}^2}} = \frac{{{H_2}}}{{{I_2}^2}}\]$

        $\[{H_1}{I_2}^2 = {H_2}{I_1}^2\]$

When, $\[{I_2} = 2{I_1}\]$

Putting value in the equation,

     $\[{H_1}{(2{I_1})^2} = {H_2}{I_1}^2\]$

     $\[{H_2} = 4{H_1}\]$.

Hence, Heat generated in the conductor will increase by a factor of 4.