3 - Series RLC Circuit
Add an inductor in series to form a RLC circuit. Set R=10Omega ,L=2.0H,C=0.05F.
Measure the voltage across the resistor as a function of the frequency in the interval 0.01 to
0.5Hz.
Note the frequency when V_(R) reaches its maximum value and if possible add a few
measurements near this value to better define the resonance frequency f_(0).
Make a graph of V_(R) vs f.
From your graph estimate f_(0)(Hz)
From equation 8 calculate f_(0).(Hz)
Find the % error of the two frequencies obtained in question 11 and 12.
The "quality" factor Q of the resonant circuit, is defined as Q=(f_(0))/(Delta )f where Delta f is the width
of the resonance curve measured between points where the power dissipation is (1)/(2) the value
at resonance. It can be shown that Q can be calculated using the expression
Q=2pi f_(0)(L)/(R)
Calculate Q
Set your frequency to the resonance frequency f_(0) (as calculated in question 12).
What is the max voltage V_(L) ? (V)
What is the max voltage V_(R) ? (V)
What is the max voltage V_(C) ? (V)
What is the voltage V_(LC) ? (V) ( V_(LC) is the voltage across the capacitor and inductor
together)
At resonance V_(L) and V_(C) should be 180deg out of phase so they would cancel and your circuit is
essential an AC source and a resistor only.
Using the current chart, what is the peak value of current in the circuit? (A)
Use the Ohm law and the impedance Z of the circuit (see Equation 7) to calculate the
peak value of the current in the circuit. (A)
Find the % error of the current obtained in two questions above.
3 - Series RLC Circuit
Add an inductor in series to form a RLC circuit.Set R = 10 , L = 2.0 H, C = 0.05 F. Measure the voltage across the resistor as a function of the frequency in the interval 0.01 to 0.5 Hz. Note the frequency when V reaches its maximum value and if possible add a few measurements near this value to better define the resonance frequency fo.
Make a graph of V vs f. 12. From your graph estimate fo.(Hz) 13.From equation 8 calculate fo.(Hz 14. Find the % error of the two frequencies obtained in question 11 and 12.
The quality factor Q of the resonant circuit, is defined as Q = fo/f where f is the width of the resonance curve measured between points where the power dissipation is / the value at resonance. It can be shown that Q can be calculated using the expression
Q= 2ufoL/R
15.Calculate Q
Set your frequency to the resonance frequency fo (as calculated in question 12) 16. What is the max voltage V? (V) 17.What is the max voltage Vr?(V) 18. What is the max voltage Vc?(V 19. What is the voltage VLc? (V(Vic is the voltage across the capacitor and inductor together)
At resonance Vi and Vc should be 180 out of phase so they would cancel and your circuit is essential an AC source and a resistor only. 20. Using the current chart, what is the peak value of current in the circuit? (A) 21. Use the Ohm law and the impedance Z of the circuit (see Equation 7) to calculate the peak value of the current in the circuit. (A) 22. Find the % error of the current obtained in two questions above.
