Question

Heat generated through a resistive wire will increase _______ times in unit time, if current in the wire becomes twice. 
1. 2
2. 4
3. 0.5
4. 0.25

Answer 1

Correct Answer - Option 2 : 4

Concept:

• A current-carrying conductor offers resistance to the coil, by which heat is generated. 
• The heat generated is given as 

H = I² Rt

or

\(H = \frac{V^2}{R}t = VIt\)

V is the potential difference, I is current, t is time, R is resistance. 

Calculation:

So heat is given by 

H = I2 Rt

time is fixed, unit time, Resistance of wire will remain the same. 

H ∝ I² 

So,

H = k I²    ---(1)

if the current becomes twice'

H' = k (2I)²    ---(2)

(2) divided by (1) we get

\(\frac{H'}{H} = \frac{4I^2}{I^2}\)

So, H' : H = 4 : 1

So we see, the heat generated in unit time becomes 4 times of its initial value.