1.) Following Activity 2-1, a 488 nF capacitor ( C ) is connected in series with
ID: 1768045 • Letter: 1
Question
1.) Following Activity 2-1, a 488 nF capacitor (C) is connected in series with a 543 ? reference resistor (R0). [See Figure 8.4 in the manual.] Vmax, the signal generator?samplitude (or magnitude or peak voltage), is set to 3.87 V and f, the generator?s frequency, is set to 45.0 Hz.
a.) The impedance of the circuit is:
b.) The amplitude of the voltage across R0 is:
c.) The amplitude of the voltage across C is:
d.) The phase shift between the current through the circuit and the driving voltage is:
Explanation / Answer
a)
Capacitive reactance
Xc=1/2pifC =1/2pi*45*(488*10^-9)
Xc=7247.5 ohms
Impedance
Z=sqrt[R^2+Xc^2]=sqrt[543^2+7247.5^2]
Z=7267.8 ohms
b)
Total current in the circuit
I=V/Z =3.87/7267.8
I=5.325*10^-4 A
Voltage across Ro is
Vr =I*Ro =5.325*10^-4*543
Vr=0.289 Volts =0.29 Volts
c)
Vc=I*Xc =5.325*10^-4*7247.5
Vc=3.86 Volts
d)
o=tan^-1(-Xc/Ro) =tan^-1(-7247.5/543)
o=-85.72 degrees
at f=772 Hz
e)
Xc=1/2pi*772*(488*10^-9)
Xc=422.46 ohms
Z=sqrt[543^2+422.46^2]
Z=687.98 ohms
f)
I=V/Z =3.87/687.98
I=5.625*10^-3 A
Vr =5.625*10^-3*543
Vr =3.05 Volts
g)
Vc =5.625*10^-3*422.46
Vc=2.38 Volts
h)
o=tan^-1(-422.46/543)
o=-37.88 degrees
For inductor
i)
Inductive reactance
XL=2pifL=2pi*45*826*10^-3
XL=233.55 ohms
Impedance
Z=sqrt[R^2+XL^2] =sqrt[543^2+233.55^2]
Z=591.1 ohms
j)
Total current
I=V/Z =3.87/591.1
I=6.547*10^-3 Volts
Vr =I*Ro =6.547*10^-3*543
Vr=3.555 Volts
k)
VL=I*XL= 6.547*10^-3*233.55
VL=1.529 Volts
l)
o=tan^-1(XL/R) =tan^-1(233.55/543)
o=23.27 degrees
at f=772 Hz
m)
XL=2pi*772*0.826
XL=4006.6 ohms
Z=sqrt[543^2+4006.6^2]
Z=4043.24 ohms
n)
I=V/Z =3.87/4043.24
I=9.57*10^-4 Amps
Vr=I*Ro=9.57*10^-4*543
Vr=0.5196 Volts
o)
VL=9.57*10^-4*4006.6
VL=3.8343 Volts
p)
o=tan^-1(4006.6/543)
o=82.28 degrees
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