How is the slope of a voltage vs time graph the current?

In summary: However, if you take the slope of the voltage vs. time graph, you do not automatically get the current.In summary, taking the slope of a voltage vs time graph does not automatically give the current. The correct formula to find the current is C*dv/d(t)=i(t), where C is the capacitance. Many websites may not mention this and could be giving incorrect information.
  • #1
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A lot of websites say that if you take the slope of a voltage vs time graph, you get the current. However, the math tells a different story.

where V = voltage, J = joules, C = coulombs, A = amperes, s = seconds

A = C / s
C = A * s
V = J / C
J = C / V

if we take the slope of Voltage vs Time, our unit is:

V/s = J/(C * s) = J / (A * s^2) = (C * V) / (A * s^2) = (C * V) / (C /s * s^2) = V/s

No matter what I do, I can never get the unit ampere.

How is it mathematically possible that the slope of a voltage vs time graph has the unit of the current? I don't get it.
 
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  • #2
x86 said:
A lot of websites say that if you take the slope of a voltage vs time graph, you get the current. However, the math tells a different story.

where V = voltage, J = joules, C = coulombs, A = amperes, s = seconds

A = C / s
C = A * s
V = J / C
J = C / V

if we take the slope of Voltage vs Time, our unit is:

V/s = J/(C * s) = J / (A * s^2) = (C * V) / (A * s^2) = (C * V) / (C /s * s^2) = V/s

No matter what I do, I can never get the unit ampere.

How is it mathematically possible that the slope of a voltage vs time graph has the unit of the current? I don't get it.
The slope does not have the units of current. The units are V/s (which can be expressed in different ways) as you have shown. Perhaps you misread the information on the websites or you looked at websites giving wrong information.
 
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  • #3
x86 said:
A lot of websites say that if you take the slope of a voltage vs time graph, you get the current.
Which websites?

However, the math tells a different story.

where V = voltage, J = joules, C = coulombs, A = amperes, s = seconds

A = C / s
C = A * s
V = J / C
J = C / V
If V = J / C then J ≠ C / V

if we take the slope of Voltage vs Time, our unit is:

V/s = J/(C * s) = J / (A * s^2) = (C * V) / (A * s^2) = (C * V) / (C /s * s^2) = V/s

No matter what I do, I can never get the unit ampere.

How is it mathematically possible that the slope of a voltage vs time graph has the unit of the current? I don't get it.
You forgot to consider capacitance.

First the variables need to be used properly.
Type______Symbol______Unit
Voltage...E...V
Current...I...A
Charge...Q...C
Capacitance...C...F
time...t...s

Q = C * E
∴ E = Q / C
E / t = Q / (C * t)
E / t = I / C
 
  • #4
x86 said:
A lot of websites say that if you take the slope of a voltage vs time graph, you get the current.
That is true for capacitors if you include capacitance as constant factor.
 
  • #5
mfb said:
That is true for capacitors if you include capacitance as constant factor.

I agree with that if you are referring to:

C*dv/d(t)=i(t)

Then yes, the slope of the voltage multiplied by the capacitance will give the current at any given time thru the capacitor.
 

FAQ: How is the slope of a voltage vs time graph the current?

1. How do you calculate the slope of a voltage vs time graph?

The slope of a voltage vs time graph can be calculated by taking the change in voltage (ΔV) divided by the change in time (Δt). This can be represented by the formula: slope = ΔV/Δt.

2. What does the slope of a voltage vs time graph represent?

The slope of a voltage vs time graph represents the rate of change of voltage over time, also known as the voltage change per unit time. This is an important measure in understanding the behavior of an electrical circuit and can help determine the current flowing through the circuit.

3. How does the slope of a voltage vs time graph relate to current?

The slope of a voltage vs time graph is directly proportional to the current flowing through the circuit. This means that as the slope increases, the current also increases. Conversely, a decrease in slope indicates a decrease in current.

4. Can the slope of a voltage vs time graph be negative?

Yes, the slope of a voltage vs time graph can be negative. This indicates a decrease in voltage over time, which can occur in certain types of circuits or when a component with resistance is added to the circuit.

5. What is the unit of measurement for the slope of a voltage vs time graph?

The unit of measurement for the slope of a voltage vs time graph is volts per second (V/s) or volts per millisecond (V/ms), depending on the time scale used for the graph. This represents the change in voltage over time and is equivalent to the unit of measurement for current, which is amps (A).

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