a. The power of an electric appliance is given by the formula P=I^2R, where I is the current and R is resistance. Use this information to explain how you can use radicals to determine the current if the power and the resistance is given.
b. Find the current in amperes if a 40-watt bulb has a resistance of 3 ohms.
P = I^2 R
plug in your given
40 = I^2 (3)
40/3 = I^2
I = √(40/3) = ...
a. To determine the current when the power and resistance are given, we can use the formula P = I^2 * R.
First, let's isolate the current (I) in the equation. Divide both sides of the equation by the resistance (R):
P / R = I^2
Now, take the square root of both sides of the equation to solve for I:
√(P / R) = I
The expression on the left side represents the square root of the ratio of power to resistance. This is where we can use radicals to find the current (I) using the given power and resistance values.
b. In this scenario, we're given that the power (P) of a bulb is 40 watts and the resistance (R) is 3 ohms.
To find the current (I) in amperes, we can use the formula derived in part a:
I = √(P / R)
Substituting the given values into the formula:
I = √(40 watts / 3 ohms)
Now, we can simplify the expression further:
I = √(13.33 A)
Taking the square root, we find that the current is approximately 3.65 amperes (A).