Experiment 7. Impedance on RLC AC circuit
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1 Experiment 7. Impedance on RLC AC circuit 1. Purpose Measure Impedance of RLC AC circuit and Confirm impedance difference with variety of frequency. 2. Principle 1) RLC device RLC device shows different behavior by output voltage occurring structural physical characteristics. Resistor has consistent electrical conductivity in DC and AC. Capacitor and inductor, on the other hand, show different behavior in DC and AC. In DC, current can t flow in capacitor. But it can easily flow in inductor because of its small resistivity. In AC, capacitor has small resistivity and inductor has large resistivity. This behavior is obvious at high frequency. This experiment will figure out physical properties of the basic circuit device by using RLC circuit. We can measure impedance in accordance with frequency. 2) Alternating Circuit Electron flows same direction in metal conductor at DC. But, electron flows one way and change to the other way in AC. This change occurs several times even during 1 sec. Voltage and current change its value on AC. This term is expressed by V = V M sinωt (1) I = I M sin(ωt + ϕ) (2) Where V M is maximum voltage, I M is maximum current, t is time, w is angle frequency and ф is initial phase. Let s consider at RLC DC as shown in Fig 1. In this circuit, V R = IR V L = LdI/dt V C = 1/C dq = 1/C Idt Therefore, AC voltage is If we substitute equations, V = V R + V L + V C = I R + LdI + 1/C Idt dt V L = ωli M cos (ωt + ϕ) V C = ( 1 C )I Mcos (ωt + ϕ) V R = RI M sin (ωt + ϕ) V L and V C has phase difference for π/2 and - π/2 from V R, respectively
2 Fig. 1. Phase difference Therefore, V M = (V RM ) 2 + (V LM V CM ) 2 We can measure maximum voltage when cos(wt+ф)=1 and -1. Let s define this values as V LM and V CM, respectively. V LM = ωli M V CM = 1 ωc I M V RM = RI M Where we define wl and 1/wC as inductive reactance X L and capacitive reactance X C, respectively. It is similar to R at Ohm s raw, V=IR in DC. X L = ωl = 2πfL X C = 1 ωc = 1 2πfC Therefore, V RM, V LM and V CM at RLC circuit is defined as V RM = I M R, V LM = I M X L, V CM = I M X C Impedance Z at AC is Z = R 2 + (ωl 1 ωc )2 And phase ф is ϕ = tan 1 V L V C V R = tan 1 ( ωl 1 ωc ) R - 2 -
3 3. Equipment and set up (1) RLC impedance measurement circuit (2) AC power supply : 0~30V, 0~1300Hz (3) 2 Multimeters (4) Resistor package (5) Capacitor package (6) Inductor package (7) Electric wire Fig 2. RLC measurement circuit - 3 -
4 4. Experiment & Results 1) R-L circuit (1) Connect one resistor and one inductor at R-L circuit. Connect electric wire at capacitor location. (2) Connect AC power supply and multimeter at circuit and put proper frequency. (proper frequency is around 10Hz~.) (3) Read current by using multimeter and record. Record voltage of power supply, resistor and inductor. (4) Measure 5 or 6 times by changing frequency. (5) Use other resistor and inductor and repeat (3)~(4). (6) Plot V R :I t, V L :I t and V t :I t. graphs. (7) Measure R, X L and Z from graphs slope. 2 (8) Confirm V R2 +V L2 =V t and impedance Z = R 2 + (wl) 2 and find ф. Plot phase transition and relation between R, Z and X L. 2) R-C circuit (1) Connect proper resistor, capacitor and electric wire. (2) Follow above experiment procedure. 3) R-L-R circuit (1) Connect proper resistor, capacitor, inductor and electric wire. (2) Follow above experiment procedure
5 5. DATA Sheet 1) R-L circuit 1st Resistor : Ω inductor : H Frequency f I t V t V R V L 2nd Resistor : Ω inductor : H Frequency f I t V t V R V L - 5 -
6 2) R-C circuit 1st Resistor : Ω capacitor : F Frequency f I t V t V R V C 2nd Resistor : Ω capacitor : F Frequency f I t V t V R V C - 6 -
7 3) R-L-C circuit 1st Resistor : Ω capacitor : F inductor: H Frequency f I t V t V R V L V C 2nd Resistor : Ω capacitor : F inductor: H Frequency f I t V t V R V L V C - 7 -
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