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In order to study the behavior of an RC circuit, I connected a resistor and a capacitor to an Arduino's I/O as shown:

enter image description here

The Arduino digital Output feeds the circuit with a square pulse of 2 sec duration. (one second HIGH, one second LOW)

for a charge time of 1 sec: $$V_c = E(1-e^{-\dfrac{t}{\tau}}) = E(1-e^{-\dfrac{1}{0.83}})=0.7E$$Converting

where E is the power supply voltage

Converting E value to a 10bit range, $$V_c = 0.7 \times 1024 = 717$$

Now, this is the graph I take from the analog input:

enter image description here

whose minimum value is 237 (0.23E), and maximum value = 784 (0.76E).

Assuming that the capacitor's value may differ a little, I may accept that 0.70E = 0.76E. But in that case, shouldn't Vc start from zero?

Assuming that the capacitor is semi charged, shouldn't in any case max-min=0.7E? (Before initiating, I discharged the capacitor connecting it with a resistor for several seconds.)

Any thoughts would be appreciated.

EDIT: Using several values of charge time, every time the graph seems to be positioned in the middle, meaning Vc(min)+Vc(max) = E/2.

In order to study the behavior of an RC circuit, I connected a resistor and a capacitor to an Arduino's I/O as shown:

enter image description here

The Arduino digital Output feeds the circuit with a square pulse of 2 sec duration. (one second HIGH, one second LOW)

for a charge time of 1 sec: $$V_c = E(1-e^{-\dfrac{t}{\tau}}) = E(1-e^{-\dfrac{1}{0.83}})=0.7E$$Converting E value to a 10bit range, $$V_c = 0.7 \times 1024 = 717$$

Now, this is the graph I take from the analog input:

enter image description here

whose minimum value is 237 (0.23E), and maximum value = 784 (0.76E).

Assuming that the capacitor's value may differ a little, I may accept that 0.70E = 0.76E. But in that case, shouldn't Vc start from zero?

Assuming that the capacitor is semi charged, shouldn't in any case max-min=0.7E? (Before initiating, I discharged the capacitor connecting it with a resistor for several seconds.)

Any thoughts would be appreciated.

In order to study the behavior of an RC circuit, I connected a resistor and a capacitor to an Arduino's I/O as shown:

enter image description here

The Arduino digital Output feeds the circuit with a square pulse of 2 sec duration. (one second HIGH, one second LOW)

for a charge time of 1 sec: $$V_c = E(1-e^{-\dfrac{t}{\tau}}) = E(1-e^{-\dfrac{1}{0.83}})=0.7E$$

where E is the power supply voltage

Converting E value to a 10bit range, $$V_c = 0.7 \times 1024 = 717$$

Now, this is the graph I take from the analog input:

enter image description here

whose minimum value is 237 (0.23E), and maximum value = 784 (0.76E).

Assuming that the capacitor's value may differ a little, I may accept that 0.70E = 0.76E. But in that case, shouldn't Vc start from zero?

Assuming that the capacitor is semi charged, shouldn't in any case max-min=0.7E? (Before initiating, I discharged the capacitor connecting it with a resistor for several seconds.)

Any thoughts would be appreciated.

EDIT: Using several values of charge time, every time the graph seems to be positioned in the middle, meaning Vc(min)+Vc(max) = E/2.

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Capacitor charge in an RC circuit

In order to study the behavior of an RC circuit, I connected a resistor and a capacitor to an Arduino's I/O as shown:

enter image description here

The Arduino digital Output feeds the circuit with a square pulse of 2 sec duration. (one second HIGH, one second LOW)

for a charge time of 1 sec: $$V_c = E(1-e^{-\dfrac{t}{\tau}}) = E(1-e^{-\dfrac{1}{0.83}})=0.7E$$Converting E value to a 10bit range, $$V_c = 0.7 \times 1024 = 717$$

Now, this is the graph I take from the analog input:

enter image description here

whose minimum value is 237 (0.23E), and maximum value = 784 (0.76E).

Assuming that the capacitor's value may differ a little, I may accept that 0.70E = 0.76E. But in that case, shouldn't Vc start from zero?

Assuming that the capacitor is semi charged, shouldn't in any case max-min=0.7E? (Before initiating, I discharged the capacitor connecting it with a resistor for several seconds.)

Any thoughts would be appreciated.