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RC Circuits and its Physical Simulation

Richard Robbins

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The Basics for RC Circuits

• The circuit that has resistors and capacitors

• The circuit that is used for timing or switching

• The differential equation is given as follows:

RI(t) + 1/C Q(t) = V(t)

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Physical Values

The initial charge is 0 coulomb.

The resistance of the resistor is 10,000 Ohms.

The voltage is 10 volts.

The capacitance of the capacitor is 1.010-6 farads

The differential equation of the RC circuit is solved by Euler’s method.

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Results

• Each graph is shown as time-dependent on the related physical values, such as charges, voltages, currents, and resistances.

• One of the variables is varied and the others are kept constant.

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Charge due to voltages (t vs.q)

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Current due to voltages (t vs. i)

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Resistance due to voltages (t vs. R)

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Charge due to capacitances (t vs. q)

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Current due to capacitances (t vs. i)

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Resistance due to capacitances (t vs. R)

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Charge due to resistances (t vs. q)

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Current due to resistances (t vs. i)

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Conclusions

According to the computational results:

• The charge accumulation in the capacitor depends on voltages and resistances as known.

• It is interesting to see the current dropping in the first time segment.

• The resistance seems going to stable after a second.