To solve this problem, we'll use the concept of joint variation and the given information to find the resistance of the refrigerator.
Let's denote:
- Power of the microwave oven as P1 = 600 watts
- Current drawn by the microwave oven as I1 = 5.0 amperes
- Resistance of the microwave oven as R1 = 24 ohms
According to the problem, the power varies jointly as the resistance and the square of the current. Mathematically, this can be represented as:
P1 = k * R1 * I1^2
where k is the constant of variation.
We can solve for k by rearranging the equation:
k = P1 / (R1 * I1^2)
Now, we'll use this value of k to find the resistance of the refrigerator:
Power of the refrigerator, P2 = 200 watts
Current drawn by the refrigerator, I2 = 1.7 amperes
Using the joint variation equation:
P2 = k * R2 * I2^2
Rearranging the equation, we get:
R2 = P2 / (k * I2^2)
Now we can substitute the known values into the equation to find the resistance of the refrigerator:
R2 = 200 / (k * 1.7^2)
First, let's calculate the value of k:
k = 600 / (24 * 5.0^2)
k ≈ 0.5
Now substitute this value into the equation for R2:
R2 = 200 / (0.5 * 1.7^2)
R2 ≈ 200 / (0.5 * 2.89)
R2 ≈ 200 / 1.445
R2 ≈ 138.31
Rounding to the nearest tenth, the resistance of the refrigerator is approximately 138.3 ohms.
