Question

8. Current through a metallic conductor is tripled while its resistance and the time are held constants. Under these conditions, the heat generated in the conductor will increase by a factor of - a) Three b) Nine c) Six d) Twelve.​

Answer 1

Explanation:

given :

• metallic conductor = triple

• resistance and the time are held = constants

to find :

• the conductor will increase by a factor = ?

• the conductor will increase by a factor = ?

solution :

• conductor = 3

formula is :

• heat = i resistance time

let us do :

• Heat ∞ ¡²

• Heat /Heat = (1')²/1²

• Heat /Heat = (31)²/1²

• Heat = 9

conductor will increase = 9

Answer 2

Given:

Current through metallic conductor = 3I (tripled)

Resistance through metallic conductor = R (constant)

Time for which current flows in conductor = t (constant)

To find:

Increase in heat generated in a conductor by what factor=?

Solution:

• An increase in heat generated in the conductor can be calculated by the following steps:
• Step 1: Use the formula for calculating the heating effect of the conductor given by Joule's law.

        => H = I²Rt (equation 1)

        Where H= Heating effect due to electric current

         I= current flowing in the conductor

        R= Resistance in the conductor

        t= time for which current flows in the conductor

• Step 2: Increase in heat generated can be written by the following formula.

        => H'= (I')²R't'

        where H'= Heating effect due to change in electric current

          I'=3I= Increased in current by three times

          R'=R

          t'=t

• Therefore we get the equation:

       => H' = (3I)²Rt. (equation 2)

• Step 3: Divide equation (1) by equation (2)

       => H' = [(3I)²Rt] ÷ H = [I²Rt]

       => H' = [9I²Rt] ÷ H = [I²Rt]

       => H' = 9(I²Rt) ÷ H = (I²Rt)

       => H' = 9

Hence, the heat generated in the conductor will increase by a factor of 9 (option b).