In circuit analysis, is current through wires defined?

In summary, the resistance of wires in a circuit is typically assumed to be 0 Ω for simplification purposes. This does not mean that the current through the wire is undefined, as it is determined by other impedances in the circuit. The current is also not considered to be zero or infinite, but rather dependent on the circuit as a whole. In reality, wires do have some finite resistance, but it is usually negligible compared to other circuit elements.
  • #1
ee15
4
0

Homework Statement


This is not a homework problem, but related to my circuits class.

In the typical electrical engineering simplification, the resistance of wires in the circuit is taken to be 0 Ω. Also, the potential difference between two points along the same wire is 0 Volts.

Does this mean that current through wires is undefined? Would engineers consider the current zero or infinite?

Homework Equations



voltage = current * resistance

The Attempt at a Solution


Maybe Ohm's Law does not apply here, and there is another way of looking at the situation.
 
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  • #2
wires in circuits generally have such a tiny resistance relative to that of the other objects in the circuit that their effect is negligible. Why would you expect otherwise? circuit analysis becomes unnecessarily complicated if you add in the tiny amounts of loss due to wires.
 
  • #3
ee15 said:
1. In the typical electrical engineering simplification, the resistance of wires in the circuit is taken to be 0 Ω. Also, the potential difference between two points along the same wire is 0 Volts.

Does this mean that current through wires is undefined? Would engineers consider the current zero or infinite?

Homework Equations



voltage = current * resistance

The Attempt at a Solution


Maybe Ohm's Law does not apply here, and there is another way of looking at the situation.


The wire can be considered to have zero resistance and the current still finite because V = IR but if R → 0 then V = 0 for any finite I. I is determined by other impedances in the circuit containing the zero-R wire.

In reality there is always some finite R for any wire (and inductance too, and some capacitance to nearby nodes ...) and for a stretch of such a wire V = IR still holds.
 
  • #4
In circuit analysis (at least when Faraday's law doesn't apply), you may assume that the wires are inexistent and that all your components connect directly where they need to.
 
  • #5
In the typical electrical engineering simplification, the resistance of wires in the circuit is taken to be 0 Ω. Also, the potential difference between two points along the same wire is 0 Volts.

Does this mean that current through wires is undefined? Would engineers consider the current zero or infinite?

Neither. You would need to consider the circuit as a whole...

In this case the resistance of the wire (0 Ohms) is going to be much less than other circuit elements that are in series with the wire. Those other circuit elements will dominate the overall resistance and the current flowing. The voltage drop down the wire is not the same as voltage source.

Imagine you have a real world battery. These behave like an ideal voltage source (Videal) in series with a small resistor representing the internal resistance of the battery (Rint). let's say that's 0.1 Ohms.

If you short out the battery using your ideal wire the current will be...

Ishort = Videal/(Rint + Rwire)

Rwire = 0 so
Ishort = Videal/Rint

The voltage drop down the ideal wire is 0V. The resistance of the wire is 0V but the current is Videal/Rint.
 

FAQ: In circuit analysis, is current through wires defined?

1. What is current and how is it measured?

Current is the flow of electric charge through a medium, such as a wire. It is measured in amperes (A) and can be calculated by dividing the amount of charge that passes through a point in a given amount of time.

2. How is current through wires defined in circuit analysis?

In circuit analysis, current through wires is defined as the amount of charge flowing through a specific point in a circuit in a given amount of time. It is typically denoted as "I" and is measured in amperes (A).

3. How is the direction of current flow through wires determined?

The direction of current flow through wires is determined by the direction of flow of positive charges. In most circuits, current flows from the positive terminal of a power source to the negative terminal.

4. What factors affect the amount of current through wires in a circuit?

The amount of current through wires in a circuit can be affected by various factors such as the voltage of the power source, the resistance of the wires, and the type of material the wires are made of. Other factors include the temperature of the wires and the presence of any components, such as resistors, in the circuit.

5. How is Kirchhoff's Current Law applied in circuit analysis?

Kirchhoff's Current Law states that the sum of the currents entering a junction in a circuit must be equal to the sum of the currents leaving that junction. This law is applied in circuit analysis to ensure that the flow of current is conserved throughout the circuit and is used in conjunction with Ohm's Law to solve for unknown currents.

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