Why is current defined as the rate of change of charge?

In summary: The net charge remains zero. It is the capacitance that stores energy as ##\frac{1}{2}CV^2##. The capacitor is a "storage tank" for energy.
  • #1
CoolDude420
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9
Homework Statement:: This isn't a homework question but just a theoretical questions.

[mentor’s note: moved to a more appropriate forum for theoretical questions.]

I know that current is defined as the rate of change of charge per unit time.
i = dq/dt

This makes sense for a capacitor which stores charge. If we define the q as being the total charge stored on the capacitor, then sure, the rate of change of the total q stored on the capacitor will tell you how much current the capacitor is receiving.

However, in this case of a resistor, this confuses me. A resistor does not store charge. If I have a DC voltage source connected across a resistor, the resistor technically should be receiving the same amount of charge for all time, hence the rate of change of charge dq/dt will always be 0, thus, i = dq/dt = 0. Does this mean that the resistor is receiving 0 current?

Where is the flaw in my understanding? I think I might be confusing instantaneous charge flowing versus total charge?
Relevant Equations:: i = dq/dt

V = IR

N/A
 
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  • #2
CoolDude420 said:
Where is the flaw in my understanding? I think I might be confusing instantaneous charge flowing versus total charge?
You are. If you use a hose to fill a bucket with water, the bucket at any time will contain ##m## kilograms of water and the hose is filling it at the rate of ##\frac{dm}{dt}## kilograms per minute. If you are charging a capacitor (bucket) using a conducting wire (hose), the capacitor at any time will have ##Q## Coulombs of charge and the wire is charging it at the rate of ##\frac{dQ}{dt}## Coulombs per minute.
 
  • #3
Please post in the regular forums when you have questions that are not homework or homework-like problems. Also, putting all of your text in the homework statement section makes it impossible to quote selected parts of it in a simple manner.

Where did you read that current is defined this way? It is not true. It is true, as you mentioned, for a capacitor (but then only for the charge on one of the plates - the total charge remains zero), but more generally current is the flow of charge per unit time.
 
  • #4
Orodruin said:
Please post in the regular forums when you have questions that are not homework or homework-like problems. Also, putting all of your text in the homework statement section makes it impossible to quote selected parts of it in a simple manner.

Where did you read that current is defined this way? It is not true. It is true, as you mentioned, for a capacitor (but then only for the charge on one of the plates - the total charge remains zero), but more generally current is the flow of charge per unit time.

Sorry, I apologies for not posting correctly.

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Fundamentals of Electric Circuits Book
 
  • #5
It may be easier for you to think of current defined as charges crossing a surface. So current is the number of charges crossing per time unit. Like charge flux.

You can define some surface in the middle of that resistor and measure the rate of charges moving across that surface. Same definition with wires, inductors, capacitors, and the solar wind in space. Yes, the capacitor stores those charges, but it's the flow (flux) you are measuring, not what happens to them, or where they end up.

PS: Sorry, I was sloppy about flow vs. flux. Flow (current) is charges/sec across a defined area. Flux (current density) is charges/(sec⋅area) at any part of the surface. Similar concepts though.
 
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  • #6
The charges are either going in or out of the capacitor through the only way in (or out). But with a resistance, there is one way in and one way out. Whatever goes in must come out such that ##i_{in} = i_{out}## or ##\frac{dq_{in}}{dt} = \frac{dq_{out}}{dt}##. So there is no accumulation of charge in the resistance.
 
  • #7
As a circuit element, a capacitor does not store net "charge" It separates charge at a relatively low potential. (It has typically two wires and the what goes in comes out.)
 
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FAQ: Why is current defined as the rate of change of charge?

1. What is current and how is it defined?

Current is the flow of electric charge through a conductor. It is defined as the rate of change of charge, or the amount of charge passing through a point in a given amount of time.

2. Why is current defined as the rate of change of charge?

This definition of current is based on the fundamental relationship between charge and electric current. As charge moves through a conductor, it causes a flow of electrons, which is what we measure as current. By measuring the rate of change of charge, we can accurately determine the amount of current flowing through a circuit.

3. Can you explain the mathematical formula for current?

The mathematical formula for current is I = Q/t, where I is current in amperes (A), Q is charge in coulombs (C), and t is time in seconds (s). This formula shows that current is directly proportional to the amount of charge passing through a point and inversely proportional to the time it takes for that charge to pass.

4. How is current measured?

Current is typically measured using an ammeter, which is a device that measures the flow of electric charge. The ammeter is connected in series with the circuit, allowing the current to flow through it and be measured. The unit of measurement for current is amperes (A).

5. Why is it important to understand the concept of current?

Understanding current is crucial in the field of electricity and electronics. It allows us to accurately measure and control the flow of electricity, which is essential for the functioning of many devices and systems. Additionally, understanding current helps us to understand other important concepts, such as voltage and resistance, which are fundamental to the study of electricity.

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