What will be the voltage drop across a 1 kW electric heater whose resistance, when hot, is 40 Ohms?
Understand the Problem
The question is asking to determine the voltage drop across a 1 kW electric heater with a known resistance of 40 ohms when it is hot. This involves applying electrical formulas related to power, voltage, and resistance.
Answer
$200 \, \text{V}$
Answer for screen readers
The voltage drop across the heater is $200 , \text{V}$.
Steps to Solve
- Identify Given Values
We know that the power ( P ) of the heater is 1 kW (which is ( 1000 , \text{W} )) and the resistance ( R ) is 40 ohms.
- Apply the Formula for Power
The formula relating power, voltage, and resistance is given by:
$$ P = \frac{V^2}{R} $$
Where ( P ) is power, ( V ) is voltage, and ( R ) is resistance.
- Rearrange the Formula for Voltage
To find the voltage ( V ), we can rearrange the formula:
$$ V^2 = P \cdot R $$
Then take the square root of both sides:
$$ V = \sqrt{P \cdot R} $$
- Substitute the Known Values
Now substitute ( P = 1000 , \text{W} ) and ( R = 40 , \Omega ):
$$ V = \sqrt{1000 \cdot 40} $$
- Calculate the Voltage
Perform the multiplication first:
$$ V = \sqrt{40000} $$
Then calculate the square root:
$$ V = 200 , \text{V} $$
The voltage drop across the heater is $200 , \text{V}$.
More Information
This calculation shows how electrical power relates to voltage and resistance. The formula used here is derived from Ohm's Law and the definition of power in an electrical circuit, linking these fundamental concepts in electricity.
Tips
- A common mistake is to forget to convert the power from kilowatts to watts. Always ensure units are consistent.
- Another mistake is mishandling square roots. Ensure you calculate the square root correctly after performing any multiplications.
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