# How much time it takes for Voltage to drop?

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1. Aug 22, 2015

### Prashan Shan

if an voltage is applied in an electric circuit connected to a resistor voltage drops across the resistor right? how much time it takes in that process?
does it occur instantly?

2. Aug 22, 2015

### Staff: Mentor

It depends on the circuit, but typical timescales are nanoseconds. The speed of light is a fundamental limit, of course.

3. Aug 22, 2015

### Prashan Shan

then lets imagine a conductor AB of length about 1 light minute, and we applied enough voltage what happens at that instant and after few seconds,
explain how current flows, and flow of electrons in that criteria.

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4. Aug 22, 2015

### nasu

How do you "apply voltage"? It seems that you consider this an instantaneous process.

5. Aug 23, 2015

### Drakkith

Staff Emeritus
The current begins to flow at each end and the voltage change in the conductor propagates at near the speed of light. The rate of change in current and voltage at any location in the conductor is not instant.

6. Aug 23, 2015

### Prashan Shan

actually my doubt is in a conductor of length 2 light minutes, lets say that end A and B are at same potential.
suddenly if the potential of end A is increased, then after few nano seconds does the electron starts to flow from any 1 of the 2 ends? (or)
will it wait till the electric field is fully established in the conductor?

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7. Aug 23, 2015

### CWatters

It might be worth thinking of the wires as a transmission line. When a voltage is applied at one end you get a step waveform that travels down the line at a speed v where v is given by..

v = c/sqrt(k)

c is the speed of light in a vacuum and
k is the relative permeability of the insulation between the conductors relative to a vacuum.

So for two wires in a vacuum k =1 and v=c.

The relative permeability of an FR4 printed circuit board is about 4.8 so v would be about c/2.

The time it takes to get to the other end can be calculated..

t = distance/velocity

so for a PCB trace/wire say 1foot (0.3m) long the time would be about 0.3 / (0.5 * 3 * 108) = 2nS.

Last edited: Aug 23, 2015
8. Aug 23, 2015

### rowny

Ideally, at the speed of light. Practically, until all capacitive elements in the circuit are charged. That could be capacitors, cables, the board, etc.

9. Aug 23, 2015

### Staff: Mentor

@CWatters, I think you put the factor of 2 at the wrong side. It should be 2 nanoseconds, not 1/2 (that would be twice the speed of light).

10. Aug 23, 2015

### CWatters

If you treat it as a transmission line it would take at least two minutes for the voltage step to arrive at the resistor end. So no current flows through the resistor until then.

There will be current flowing from the source into parasitic capacitance between the wires before then.

11. Aug 23, 2015

### CWatters

Thanks, I've corrected my post. I thought 0.5nS seemed a bit short.