The heat in unit H produced by a battery current is directly proportional to time t and the square of the voltage v and inversely as the resistance R ,when H=120, t=2 v=24, R=80

(I) what is the law connecting the variable
(ii) calculate H when t= 3/2 v=120 and R= 60?

H = ktV^2/R

plug in your point to find k

So, HR/tV^2 = k, is constant
You want H such that
60H/(3/2 * 120^2) = (120*80)/(2*24^2)

I don't know how to solve it

I dont no how to solve it

H = k t v 2

To find the law connecting the variables, we can start by analyzing the information given in the problem. We are told that the heat, H, produced by a battery current is directly proportional to time, t, and the square of the voltage, v, and inversely proportional to the resistance, R.

Based on this information, we can write the following equation:

H ∝ t * v^2 / R

To introduce the constant of proportionality, we can rewrite the equation as follows:

H = k * t * v^2 / R

Now, let's move on to calculating the value of H when t = 3/2, v = 120, and R = 60.

Plug in the given values into the equation:

H = k * (3/2) * (120)^2 / 60

Simplify the equation:

H = k * (3/2) * 14400 / 60

H = k * 21600 / 60

H = k * 360

Since we don't know the exact value of the constant of proportionality (k), we won't be able to calculate the specific value of H. However, we can determine the relationship between H and the other variables.

From the equation, we can see that if the time (t) is doubled, the heat (H) will also double. Similarly, if the voltage (v) is quadrupled, the heat (H) will increase by a factor of 16. Finally, if the resistance (R) is halved, the heat (H) will double.

Therefore, the law connecting the variables is that the heat (H) is directly proportional to time (t), the square of the voltage (v), and inversely proportional to the resistance (R).

To calculate the specific value of H, we would need to know the value of the constant of proportionality (k).