1.) Consider an RC series circuit. You measure R to be 881 ? and C to be 810 nF.

Question

1.) Consider an RC series circuit. You measure R to be 881 ? and C to be 810 nF. You set the signal generator output to produce a sinusouidal output with an amplitude of 1.85 V.

i) At what frequency will XC equal R?

ii) What will the voltage across the capacitor be at this frequency?

Now we produce a driving signal that is the sum of a 49.1 Hz sinusoid with an amplitude of 1.84 V and a 779 Hz sinusoid with an amplitude of 2.05 V.

iii) Answer the following: What will the ratio of the amplitude of the voltage across the resistor due to the 49.1 Hz component of the signal to that of the 779 Hz component?

Explanation / Answer

a)

Given

Xc=R

since

Xc=1/2pifC

1/2pifC =R

=>f=1/2pi*R*C

f=1/2pi*881*(810*10^-9)

f=223.03 Hz

b)

Impedance

Z=sqrt[R^2+Xc^2]

Z=sqrt[881^2+881^2]

Z=1245.92 ohms

Total current in the circuit

I=V/Z =1.85/1245.92

I=1.4848*10^-3 Amp

so

Voltage across CaPACITOR IS

Vc=I*Xc =1.4848*10^-3*881

Vc=1.308 Volts

c)

at f=49.1 Hz

Xc=1/2pi*f*C =1/2pi*49.1*(810*10^-9)

Xc=4001.8 ohms

Impedance

Z=sqrt[R^2+Xc^2]=sqrt[881^2+4001.8^2]

Z=4097.6 ohms

Current

I=V/Z =1.84/4097.6

I=4.49*10^-4 Amp

Voltage across resistor

V1 =I*R =4.49*10^-4*881

V1=0.3956 Volts

at f=772 Hz

Xc=1/2pi*772*810*10^-9

Xc=254.5 ohms

Z=sqrt[881^2+254.5^2]

Z=917.02 ohms

I=V/Z =2.05/917.02

I=2.235*10^-3 A

so Voltage across resistor

V2=2.235*10^-3*881

V2=1.97 Volts

so ratio

V1/V2 =0.3956/1.97

V1/V2=0.2

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