Understand Kirchoff's Loop Law: Voltage & Circuit Elements

[G01]

I'm having some trouble understanding Kirchoff's loop law. I understand that it is a statement of conservation of energy, and I understand this. My problem comes when we start talking about circuit elements. If we had a shorted battery, the electrons moving through the circuit would loss there potential as they went around. Now let's add a resistor. The law states that the voltage lost in the resistor is equal to the emf of the battery. Why is this? To me it seems that the electrons lose their potential whether there is a circuit element there or not. How can we be sure that all the potential is lost in the resistor? Thank you for you help.

 

[Andrew Mason]

I'm having some trouble understanding Kirchoff's loop law. I understand that it is a statement of conservation of energy, and I understand this. My problem comes when we start talking about circuit elements. If we had a shorted battery, the electrons moving through the circuit would loss there potential as they went around. Now let's add a resistor. The law states that the voltage lost in the resistor is equal to the emf of the battery. Why is this? To me it seems that the electrons lose their potential whether there is a circuit element there or not. How can we be sure that all the potential is lost in the resistor? Thank you for you help.

In a circuit containing a battery one has to take into account the internal resistance of the battery. If you short a battery, the current is not infinite. You can think of the battery as a voltage source with a small resistor in series. As you increase the current, there is a drop in the voltage across the battery terminal and the battery will get warm.

So Kirchoff's voltage law applies. You just have to take into account the internal resistance. In other words, the voltage across the external resistor is equal to the emf of the battery minus the voltage drop across the internal resistance of the battery. This voltage drop depends on the current (V=IR) so for a high applied resistance (low current), the voltage drop across the battery will be small.

AM

 

[kyle8921]

Kirchoff's loop law is a fundamental principle in circuit analysis that states that the sum of the voltage drops around any closed loop in a circuit is equal to the sum of the voltage sources in that loop. This law is based on the principle of conservation of energy, which states that energy cannot be created or destroyed, only transferred.

In the case of a shorted battery, the electrons will indeed lose their potential as they move through the circuit. However, this potential loss is not due to the presence of a circuit element, but rather the short circuit itself. In a short circuit, the resistance of the circuit is extremely low, causing a large current to flow. This results in a significant voltage drop across the short circuit, leading to a loss of potential for the electrons.

When a resistor is added to the circuit, the voltage drop across the resistor is equal to the emf (electromotive force) of the battery. This is because the resistor adds resistance to the circuit, limiting the flow of current. As a result, the voltage drop across the resistor is proportional to the amount of current flowing through it, which is determined by the emf of the battery. Therefore, the voltage drop across the resistor is equal to the emf of the battery, as stated by Kirchoff's loop law.

To ensure that all potential is lost in the resistor, we can use a voltmeter to measure the voltage drop across the resistor. This will confirm that the voltage drop is equal to the emf of the battery. Additionally, the law of conservation of energy ensures that the total energy in the circuit is conserved, so any potential lost in the resistor must be accounted for by the emf of the battery.

In summary, Kirchoff's loop law is a fundamental principle in circuit analysis that helps us understand the relationship between voltage, current, and circuit elements. It is based on the principle of conservation of energy and can be verified through experimental measurements. With a better understanding of this law, you will be able to analyze and design more complex circuits in the future.