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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