Q on Heat and Electricity?

Question

H = I.I.R.T
i.e. H is directly proportional to R

Also, H = V.V.T / R
i.e. H is inversely proportional to R....

How is this possible? Please explain...

Answer 1

By taking the base unit of I.I.R.T and V.V.T/R, you will find out that both of them are [kg^-1 m^2 s^-2] which prove that both equation are equivalent.

A second method will be substituting:
I=V/R

By substituting the equation above on your first equation, you will have the second equation.


More ever, it is not right to say that H is directly proportional to R by simply not caring for the current.
It is because that the current, voltage and resistance are inter-related. Hence the 2 statement that H is proportional to R is false in the first place

Answer 2

In math, I = V / R, so when you replaced the two I.I in the first equation you get two V.V / R.R in the second equation, only one of the two R.R in the denominator cancels the R in the numerator, so the net effect appears to invert the R.

In words, H is directly proportional to R given a fixed current and invertly proportional to R given a fixed voltage.

Answer 3

V=I*R

Therfore

I=V/R

In the first equation,

H= I*I*R*T (sub in I*R=V) = I*(I*R)*T= I*V*T (sub in I=V/R) =(V*/R)V*T = V*V*T/R