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The power, in watts, of an electrical circuit varies jointly as the resistance and the

square of the current. For a 600-watt microwave over that draws a current of 5.0
amperes, the resistance is 24 ohms. What is the resistance of a 200-watt refrigerator
that draws a current of 1.7 amperes (round to the nearest tenth)?

User Bruria
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1 Answer

4 votes

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.

User Jeremy Condit
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