The heating element of an electric oven is designed to produce 3.3 kW of heat when connected to a 240-V source. What must be resistance of the element?
To determine the resistance of the heating element, we can use Ohm's Law, which states that the current flowing through a conductor is equal to the voltage across it divided by its resistance.
The formula for Ohm's Law is:
I = V / R
Where:
- I is the current in Amperes (A)
- V is the voltage in Volts (V)
- R is the resistance in Ohms (Ω)
Given:
- The voltage (V) is 240 V
- The power (P) is 3.3 kW
The power (P) can be calculated using the formula:
P = V * I
We can rearrange the formula to solve for the current (I):
I = P / V
Substituting the given values:
I = 3300 W / 240 V
I ≈ 13.75 A
Now we can use Ohm's Law to calculate the resistance (R):
R = V / I
R = 240 V / 13.75 A
R ≈ 17.45 Ω
Therefore, the resistance of the heating element should be approximately 17.45 Ω.
To find the resistance of the heating element, we can use Ohm's law, which states that the current (I) flowing through a component is equal to the voltage (V) across the component divided by the resistance (R). Mathematically, it is represented as:
I = V / R
In this case, we know the voltage (V) is 240 V and the power (P) of the heating element is given as 3.3 kW. Power is related to voltage and current by the equation:
P = V * I
Since we are given the power and voltage, we can rearrange the equation to solve for the current (I):
I = P / V
Let's substitute the given values into the equation to find the current:
I = 3.3 kW / 240V = 3300 W / 240 V
Now that we have the current, we can rearrange Ohm's law to solve for resistance (R):
R = V / I
Substituting the given values:
R = 240 V / (3300 W / 240 V)
Simplifying the expression:
R = (240 V)^2 / 3300 W
Therefore, the resistance of the heating element is (240 V)^2 / 3300 W.