Physics High School

knowing the arduino runs at 16mhz, we can estimate that time it takes to reach the cap threshold (or the time it takes the capacitor to charge up to the on voltage of 2.5v) is 1/16e6*cap threshold. knowing this information and the value of your resistor, calculate the value of capacitance needed for the circuit to sense that the sense pad has been touched. hint – use the first-order response equation).

Answers

Answer 1

To calculate the value of capacitance needed for the circuit to sense that the sense pad has been touched, we need to use the first-order response equation. The equation for the first-order response of an RC circuit is given by:

[tex]V(t) = Vf(1 - e^(-t/RC))[/tex]
In this equation, V(t) represents the voltage across the capacitor at time t, Vf is the final voltage (in this case, 2.5V), e is the base of the natural logarithm, t is the time, R is the resistance, and C is the capacitance.

We are given that the time it takes for the capacitor to charge up to the on voltage of 2.5V is 1/16e6 * cap threshold, where cap threshold represents the capacitance threshold.

To calculate the capacitance, we can rearrange the equation and solve for C:

[tex]V(t) = Vf(1 - e^(-t/RC))[/tex]
[tex]2.5V = 2.5V(1 - e^(-t/RC))\\[/tex]
[tex]1 = 1 - e^(-t/RC)[/tex]
[tex]e^(-t/RC) = 0[/tex]
Since the exponential term is equal to zero, this implies that the time constant t/RC is infinite. Therefore, the capacitance required to sense that the sense pad has been touched is infinite.

The value of capacitance needed for the circuit to sense that the sense pad has been touched is infinite. This means that the capacitance should be very large.

The capacitance needed for the circuit to sense that the sense pad has been touched depends on the time constant of the RC circuit. The time constant is given by the product of the resistance (R) and the capacitance (C). In this case, the time it takes for the capacitor to charge up to the on voltage of 2.5V is given as 1/16e6 * cap threshold.

However, when we solve for the capacitance using the first-order response equation, we find that the capacitance required is infinite. This means that the capacitance should be very large in order for the circuit to sense that the sense pad has been touched.

The capacitance needed for the circuit to sense that the sense pad has been touched is infinite or very large.

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Related Questions

Why did it take more generations of complete selection to reduce q from 0.1 to 0.01 (a 0.09 change) compared that for a 0.5 to 0.1 reduction (a larger, 0.4 change)? explain.

Answers

In conclusion, the starting frequency of a trait determines how many generations of complete selection are needed to reduce its frequency. A higher starting frequency allows for a faster reduction, while a lower starting frequency requires more generations for the same amount of change.

The reason it took more generations of complete selection to reduce q from 0.1 to 0.01 compared to reducing it from 0.5 to 0.1 is because of the starting frequencies of q.
When starting with a higher frequency of q, such as 0.5, there is a larger pool of individuals with the desired trait. This means that there are more individuals available for selection and reproduction, which can lead to a faster reduction in the frequency of q.
In contrast, starting with a lower frequency of q, such as 0.1, means that there are fewer individuals with the desired trait. This smaller pool of individuals results in a slower rate of selection and reproduction, leading to a slower reduction in the frequency of q.
To put it simply, it is easier and faster to reduce a trait that is more common in a population compared to one that is less common.
In conclusion, the starting frequency of a trait determines how many generations of complete selection are needed to reduce its frequency. A higher starting frequency allows for a faster reduction, while a lower starting frequency requires more generations for the same amount of change.

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