A Resistor and a Capacitor in a Series AC Circuit A resistor

A Resistor and a Capacitor in a Series AC Circuit

A resistor with resistance R and a capacitor with capacitance C are connected in series to an AC voltage source. The time-dependent voltage across the capacitor is given by VC(t)=VC0sint.

Part A

What is the amplitude I0 of the total current I(t) in the circuit?

Express your answer in terms of any or all of R, C, VC0, and .

CVc0

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Solution

Vc = Vcosin(wt)

Total voltage = V(t)

V(t) = IR + Vc

and Io = Vo/Z = (IR + Vcosin(wt))max/Z = (IoR + Vco)/sqroot(R^2 + 1/w^2C^2)