Download RC cuircuit using oscilloscope

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Transcript
EXPERIMENT 4:Studying RC characteristic using
Oscilloscope and Multimeter
Debangshu Mukherjee
BS.c Physics,1st year
Chennai Mathematical Institute
10.10.2008
1
Aim of experiment
The aim of the experiment is to get acquianted with the instruments oscilloscope and multimeter and hence determine the capacitance by studying
the variation of of reactance with frequency
2
Apparatus required
a)Oscilloscope
b)Connecting wires
c)Capacitor
d)Resistor
e)AC source
3
Theory of experiment
For the first part, we supply a definite frequency through the function generator. We get a corressponding waveform in the oscilloscope screen. We
measure the time period. Corresspondingly, we find the frequency ν. They
should be roughly equal. The RC circuit consists of a Capacitor and a Resistor connected in series supplied by a AC power supply in form of a Function
Generator. As the supplied is sinusoidal,the current in each element is also
sinusoidal,but are not in phase. A series combination of a resistor R and
capacitor C if connected to AC source of angular frequency f and RMS voltage V, the RMS current flowing in the circuit is given by I = VR /R, where
VR is the voltage across the resistor. If, VC is the RMS voltage across the
capacitor, then VC = ZC I also C = 2πf1XC . The voltage acrosss an ideal
capacitor lags the current by 90◦ .
1
4
Procedure
The oscilloscope is connected with the function generator. We supply an
input frequency. The readings are noted from oscilloscope and the ν is calculated. The intensity of current is measured from the CRO by calculating
the peak to peak value in each waveform. Now, the RMS value of AC current is measured using a multimeter. The ratio of peak value of current
√ to
Ipeak
RMS value should come out to be ≈ 1.414. This is because, IRM
=
2.
S
For the second part, a circuit is constructed as follows with the resistor and
capacitor in series with the oscilloscope measuring the potential drop across
the two.
We, connect the two oscilloscope across the capacitor as well as resistance
to get the RC charactristics. If, the phase difference between Vc and VR
is φ, then cosφ = VR = R
Z . We obtain the value of current vs voltage
characteristic of a capacitance. From this data, we plot impedance (Zc ) vs
voltage. Thus, we can obtain the capacitance value. The capacitance can
be obtained by by plotting Z1c vs frequency i.e ν. Finally, we plot a phasor
diagram with VR ,VC and V and obtain the capacitance loss factor.
5
Calculations
In the first part, even when we change the frequency, the amplitude is constant. This proves, current is independent of frequency. Moreover, the
R.M.S value is √12 times the peak value.
Measurement for capacitance
S.No
1
2
3
4
5
R(Ω)
1000
1000
1000
1000
1000
Freq(ν)(in Hz)
1010
904
874
802
758
VR
12.02
12.24
12.74
13.46
13.62
V
12.20
12.50
13
13.80
14
C(in µF)
0.91
0.85
0.90
0.87
0.88
Thus, the average capacitance is 0.882 µF. Though the capacitor was marked
to be 1µF, yet due to temperature, loss factor and other effects, it came out
to be 0.882µF.
6
Result
Average capacitance is 0.882µF.
2