# Single Loop Circuit Energy Conservation

• breez
In summary, according to the principle of conservation of energy, the work done by an ideal battery in a single loop circuit must be equal to the thermal energy produced in the resistor. This is due to the fact that energy is always conserved and cannot be created or destroyed. It is also a result of Ohm's law, where voltage is converted into heat energy. While some voltage may have been converted into kinetic energy, the overall energy in the system remains constant. Mathematically, this can be represented by the equation W = QV, where W is work, Q is charge, and V is voltage.
breez
My physics textbook states the following about a single loop circuit with a resistor and ideal battery.

"From the principle of conservation of energy, the work done by the (ideal) battery must equal the thermal energy that appears in the resistor"

Can anyone explain why energy must be conserved? Isn't the battery producing an applied force on the charges? How can we be sure this applied force is a conservative force? Also even if energy is conserved, why must the thermal dissipation equal the work done by the battery?

Energy is always conserved by definition. If energy is not conserved then we create a new type of energy so it is.

In this case, current is never "lost", but voltage (electromotive force) is. That "voltage" is "converted" into heat energy and so it remains conserved. It's a simple application of ohm's law.

But couldn't some of the voltage have gone into the kinetic energy of the charges? How would you write out mathematically the conservation of energy in this case?

## 1. What is a single loop circuit?

A single loop circuit is an electrical circuit that has a single path for current to flow through. It consists of a power source, such as a battery, and a load, such as a light bulb, connected by a single wire.

## 2. How does energy conservation apply to a single loop circuit?

In a single loop circuit, energy conservation refers to the principle that the total amount of energy entering the circuit (from the power source) must be equal to the total amount of energy leaving the circuit (to the load). This is known as the law of conservation of energy.

## 3. What are the components of a single loop circuit?

The basic components of a single loop circuit include a power source, a load, and a conductor (usually a wire) connecting the two. Additional components, such as switches and resistors, may also be included depending on the specific circuit design.

## 4. Why is energy conservation important in single loop circuits?

Energy conservation is important in single loop circuits because it ensures that the circuit operates efficiently and safely. If the amount of energy entering the circuit is greater than the amount leaving, it can lead to overheating and potential damage to the components. Additionally, proper energy conservation allows for the effective use of energy resources.

## 5. How can energy conservation be achieved in a single loop circuit?

Energy conservation in a single loop circuit can be achieved by using components with appropriate resistance values, ensuring proper wiring and connections, and using energy-efficient devices. It is also important to properly size the power source for the load to avoid excess energy consumption.

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