Question

What will be the percentage change in generated heat of a heating coil if the current through the coil is halved and the length of the coil is doubled for an unit time.

• A. 20%
• B. 50%
• C. 40%
• D. 46%

Answer 1

The correct option is B

50%

Given:
H = heat generated in the coil
I = current through the coil
R = resistance of the coil
unit time t = 1sec
let, length of the coil = l, area of coil = A, resistivity of material of the coil =
Now, if legth of the coil is doubled, new coil length is 2(l)
the new resistance of coil is R' = 2R.
Now if the current is halved, new current in the coil I' = $\frac{I}{2}$

Now heat generated in the coil H' = $I^{\prime 2}$ $\times$ R' $\times$ t
or H' = $\frac{I^2}{4}$ $\times$ 2R $\times$ t
= $\frac{1}{2}$ $\times$ $I^2$ $\times$ R $\times$ t
or, H' = $\frac{1}{2}$ (H)
So, the new heat generated H' is half of the heat being generated in the coil previously H.
The percentage change in new heat generatd is 50% decrease.