The wattage rating of an appliance W varies jointly as the square of the current I and the resistance R. If the wattage is 1.5 watts when the current is 0.1 ampere and the resistance is 150 ohms, find the wattage when the current is 0.3 ampere and the resistance is 50 ohms.
W = i^2 R (what else is new?)
1.5 = .01 R
R = 150 Ohms
W = .3^2 (50) = 4.5 Watts
or using just proportions
W = 1.5 (.3/.1)^2 * 50/150
= 1.5 * 9/3 = 1.5*3 = 4.5 Watts, remarkable :)
To find the wattage, we can use the formula for joint variation:
W = k * I^2 * R
where W is the wattage, I is the current, R is the resistance, and k is the constant of variation.
First, we can find the value of k using the given values of wattage, current, and resistance:
1.5 = k * (0.1)^2 * 150
Solving this equation for k, we get:
k = 1.5 / (0.1^2 * 150)
Now we can use the value of k to find the wattage for the new values of current and resistance:
W = k * (0.3)^2 * 50
Substituting the value of k and simplifying the equation, we get:
W = (1.5 / (0.1^2 * 150)) * (0.3)^2 * 50
Calculating this expression, the wattage is:
W ≈ 3.375 watts
To find the wattage when the current is 0.3 amperes and the resistance is 50 ohms, we can use the formula for joint variation:
W = k * I^2 * R
where W is the wattage, I is the current, R is the resistance, and k is the constant of variation.
We are given that the wattage is 1.5 watts when the current is 0.1 amperes and the resistance is 150 ohms. We can use this information to find the constant of variation, k.
Using the given values, we have:
1.5 = k * (0.1)^2 * 150
Simplifying this equation:
1.5 = k * 0.01 * 150
1.5 = 1.5 * k
Dividing both sides by 1.5, we get:
k = 1
Now that we have the value of k, we can substitute it into the formula to find the wattage when the current is 0.3 amperes and the resistance is 50 ohms:
W = 1 * (0.3)^2 * 50
W = 1 * 0.09 * 50
W = 4.5 watts
So, the wattage when the current is 0.3 amperes and the resistance is 50 ohms is 4.5 watts.