# How long does it take to reach 50% of V1?

• Matt Howard
In summary, the best way to find out the time it takes for the capacitor to reach 50% of V1 is by using the formula V=V_s(1-e^(-t/T)) for charging and V=V_0(e^(-t/T)) for discharging. By setting the capacitor voltage to 7 volts, the equation can be simplified to 7=14-14e^(-t/1.7x10^-3). Solving for t, the time is 1.18 ms. It is important to note that this calculation assumes the switch is moved from the lower position to the upper position at t=0.
Matt Howard
I'm unsure of the best way to go about finding out the time it takes for the capacitor to reach a voltage of 50% of V1.

V1: 14V
Resistor before 2pt switch: 1K ohm
Resistor after 2pt switch: 220 ohm
(Charging) 1 time constant is 1.7mS
(Discharging) 1 time constant is 308 micro seconds

I've attached a picture of the circuit with the values labelled.
Is there an equation for working this out or is there a specific way of working it out? Any help or suggestions are greatly appreciated - I'm not looking for anyone to do the work for me just looking for a jab in the right direction

I thought I could work it out based on the idea that at 1TC the capacitor has reached 63% of the supply voltage (8.82V) and working out the difference there but kept getting myself in a right muddle.

You know that charging a capacitor goes according to $V=V_{s}(1-e^{\frac{-t}{T}})$? And discharging goes as $V=V_{0}(e^{\frac{-t}{T}})$?

I think I vaguely remember that from class. so for me it would be something like: 7=14(1-e-t/1.7x10-3)? Is that right?
I'm assuming it's t I'm looking for so how would I go about transposing that to solve for t?

Matt Howard said:
I think I vaguely remember that from class. so for me it would be something like: 7=14(1-e-t/1.7x10-3)? Is that right?
I'm assuming it's t I'm looking for so how would I go about transposing that to solve for t?
What have you tried?

There's some algebraic simplifications which can be done the equation before solving for t.

So simplified is 7=14-14e-t/1.7x10-3

The only idea I could find (Until Svein commented) was working it out from the fact that the capacitor is 63% charged when 1 time constant had lapsed. I worked out the voltage from that and thought I could work out the time from the differences in percentage and voltage. I.e a very confusing way of doing it that a friend suggested.

Matt Howard said:
So simplified is 7=14-14e-t/1.7x10-3

Yep, that is correct.

Solve for t.

ln .5 = -t/(1.7E-3)

t = 1.18 ms.

Matt Howard said:
So simplified is 7=14-14e-t/1.7x10-3

The only idea I could find (Until Svein commented) was working it out from the fact that the capacitor is 63% charged when 1 time constant had lapsed. I worked out the voltage from that and thought I could work out the time from the differences in percentage and voltage. I.e a very confusing way of doing it that a friend suggested.

This sounds like nonsense. Setting the capacitor voltage to 7 volts in the formula is good. What is said above probably isn't going to do you any favors.
You don't care when it's charged, you just care when it's 7 volts.

The assumption being made is that the switch is moved from its lower position (shown) to its upper position at t=0. Is that what you're told?

I ask only because a different switching scenario is possible.

That is correct, the switch is being moved from the lower position to the upper position at t=0

So ... you're all sorted now?

The unfamiliar step was that where you need to take natural logarithms of both sides, in the process losing the exponential function.

Yes, I am sorted now, thank you very much! I have now completed the work, thanks again!

NascentOxygen

## 1. How is V1 defined and measured?

V1, also known as the visual cortex, is a region in the brain responsible for processing visual information. It is commonly measured using various neuroimaging techniques such as fMRI or EEG.

## 2. What factors can affect the time it takes to reach 50% of V1?

The time it takes to reach 50% of V1 can be affected by various factors such as the complexity of the visual stimulus, the individual's level of attention, and their overall cognitive ability.

## 3. Is there a standard time frame for reaching 50% of V1?

No, there is no standard time frame for reaching 50% of V1 as it can vary depending on the individual and the specific task or stimulus being presented.

## 4. Can this measurement be used to diagnose any neurological conditions?

The measurement of reaching 50% of V1 is not typically used for diagnosing neurological conditions. It is often used in research studies to understand the brain's response to visual stimuli.

## 5. How can this information be applied in real-world situations?

Understanding the time it takes to reach 50% of V1 can provide valuable insights into how the brain processes visual information. This can be applied in various fields such as education, advertising, and design to optimize visual stimuli for maximum impact.

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