# Calculating the Ampere Rating of a Circuit Breaker

• dewdrop714
In summary: JIn summary, the owner of a greenhouse uses 800kg of water in barrels to save on heating costs. The water is heated by the sun during the day to 50 degrees Fahrenheit and freezes into ice at 32 degrees Fahrenheit during the night. The solution to the problem involves calculating the minimum ampere rating for a 240 volt circuit breaker to avoid tripping, which is found to be 62.77Amperes. To determine the heat energy of the water and ice, the specific heat of water and the heat of fusion of water are used in calculations. The final result is 5.42*10^6 J. However, a correction is made to use the specific heat of water over 10°C and the
dewdrop714
The problem statement:
To save on heating costs, the owner of a greenhouse keeps 800kg of water around in barrels. During a winter day, the water is heated by the sun to 50 degrees Fahrenheit. During the night the water freezes into ice at 32 degrees Fahrenheit in 10 hours. An electrical heating system is used providing the same heating effect as the water.

The attempt at a solution:

P=Q/t = (542*10^6)/36000s = 15066 Watts
I=P/V = 15066/240 = 62.77Amperes

The minimum ampere rating that the 240 volt circuit breaker would have to be to avoid tripping is what i calculated...it turned out to be 62.77Amperes.

The question:
What I don't get is "does the circuit breaker trip? Why or why not?"

How did you arrive at the 5.42*106 J for Q?

Well 4186 is spec heat of water and 2093 is spef heat of ice. I also converted the temps to kelvins. Then I input them into the equations...I did Q1= (800)(4186)(305.93)=102*10^7 and Q2=(800)(2093)(287.93)=482*10^6. Then i got Q= Q1-Q2 = 542*10^6.

First of all I would just convert to °C making 50°F = 10°C

Next I would point out that what you have is a Specific heat of water over 10°C + the heat of fusion of water, not the specific heat of ice as there is no change in ice temp below 0°.

http://230nsc1.phy-astr.gsu.edu/hbase/thermo/phase.html#c1

That would be :

Q = (ΔC*4186j/°Ckg + 334*103J/kg)*800kg
Q = (10*4186 + 334,000)*800 = 3.7586*105*800 = 3*108

## 1. How do I calculate the ampere rating of a circuit breaker?

To calculate the ampere rating of a circuit breaker, you need to determine the maximum current that will flow through the circuit. This can be done by adding up the amperage ratings of all the devices and appliances connected to the circuit. Once you have this total, you can then choose a circuit breaker with an ampere rating that is equal to or slightly higher than this total.

## 2. What factors should I consider when calculating the ampere rating of a circuit breaker?

When calculating the ampere rating of a circuit breaker, you should consider the type of circuit (residential, commercial, or industrial), the size and length of the wire used in the circuit, and the type and number of devices and appliances connected to the circuit. Additionally, you should also take into account any potential future expansions or additions to the circuit.

## 3. Can I use a circuit breaker with a higher ampere rating than the total current of my circuit?

No, it is not recommended to use a circuit breaker with a higher ampere rating than the total current of your circuit. This can create a safety hazard as the circuit may not be able to handle the higher current and could potentially overload and cause a fire or damage to your electrical system.

## 4. What are the consequences of using a circuit breaker with a lower ampere rating than the total current of my circuit?

If a circuit breaker with a lower ampere rating is used, it may trip frequently or even fail to protect the circuit in case of an overload. This can lead to potential safety hazards such as electrical fires. It is important to always use a circuit breaker with an ampere rating that is equal to or slightly higher than the total current of the circuit.

## 5. Do I need to consider the ambient temperature when calculating the ampere rating of a circuit breaker?

Yes, the ambient temperature can affect the ampere rating of a circuit breaker. Most circuit breakers are designed to operate at a maximum ambient temperature of 40°C (104°F). If the temperature is higher than this, the ampere rating of the circuit breaker may need to be reduced to ensure its proper functioning.

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