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RC series circuit

Problem 6. Consider the simple circuit shown below.
The voltage source provides V1(t) = 100 cos (wt) Volts.

a) Define reference directions for voltages and currents.
b) Write down a complete set of linearly independent equations for the phasor quantities in this circuit.
c) Solve these equations to find the expressions for the phasors corresponding to the voltages across the resistor and the capacitor.
d) Find the expressions for the real time dependent voltage across the capacitor.
f) At what frequency of the AC source (in Hz) is the amplitude of the voltage across the capacitor (as measured by the probe) equal to 50 Volts.
g) At the frequency found in part f. what is the phase of voltage across the capacitor.
h) What is the amplitude and phase of the current flowing through the circuit.

(see diagram in attached file)

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It provides examples of analyzing a RC series circuit. The solution is detailed and was rated '5/5' by the student who originally posted the questions.

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