Final answer:
The resistance of the heating element in a 500 W electric kettle that carries a current of 4.0 A is calculated using the power formula P = VI and Ohm's law V = IR, resulting in a resistance of 31.25 ohms.
Step-by-step explanation:
To calculate the resistance of the heating element in a 500 W electric kettle that carries a current of 4.0 A, we can use Ohm's law, which states that the voltage (V) across the element is equal to the product of the current (I) flowing through it and the resistance (R) of the element. The formula for power (P) can also be used, which states that P = VI, where power is in watts, voltage is in volts, and current is in amperes.
Since the power is given (500 W), and we know the current (4.0 A), we can rearrange the formula for power to solve for voltage: P = VI becomes V = P/I. From Ohm's law (V = IR), we know that V/I = R, hence R = P/I2.
Plugging in the given values, we get:
R = 500 W / (4.0 A)2 = 500 W / 16 A2 = 31.25 Ω
So, the resistance of the heating element is 31.25 ohms.