Calculate phasor of voltage in circuit

[Name15]

Homework Statement

Calculate phasor of the output voltage (Vout). The circuit is powered by a sine wave voltage source (Vs) with amplitude=10V and frequency=1000Hz.

Homework Equations

Voltage= Current*Impedance (V=IZ)
Z(R) = R
Z(C) = 1/jwC
i(t) = Acos(wt - phi)
V(out)=[Z(C) / (R+Z(C))]*Vs

The Attempt at a Solution

Total capacitance = 6.8nF+15nF=21.8nF
Z(R)=1000 Ohms
Z(C)=(-j)(1/(1000*21.8nF) = -45870j
Vout = [Z(C) / (R+Z(C))]*Vs = 0.98*Vs

 

[gneill]

The capacitors are not in parallel; R1 is between their top connectors.

Hint: You should note that C1 is connected directly across the voltage source. Does C1 affect the rest of the circuit in any way?

 

[Name15]

ah ok thanks. I always struggle to differentiate between series and parallel. However, is the final equation I used correct?

 

[gneill]

ah ok thanks. I always struggle to differentiate between series and parallel. However, is the final equation I used correct?

Yes, if you use the right value for the capacitance when calculating it.

 

[Name15]

I'm actually unsure what Vs is?

 

[gneill]

Vs(t) is described as a 10 V amplitude sinewave with a frequency of 1000 Hz. What's the phasor of a sinewave?

 

[Name15]

v(t)= A sin(ω t + φ)?

 

[gneill]

v(t)= A sin(ω t + φ)?

No, that's the original time domain form. What do your class notes or text say?

 

[Name15]

we didn't really cover this in much detail. Is it Ae^jφ

 

[gneill]

we didn't really cover this in much detail. Is it Ae^jφ

So in this case there's no phase shift specified for the sinewave, making φ equal to zero. What does that leave?

 

[Name15]

just A, which is 10v? so Vs is simply 10v?

 

[gneill]

just A, which is 10v? so Vs is simply 10v?

Yes. The phasor representation for a sinewave without a phase shift is simply the amplitude of the sinewave.