# Lab2 - Julia Bielaski 0163140 Lab Report#2 PH 327 Objective...

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Unformatted text preview: Julia Bielaski 0163140 Lab Report #2 PH 327 Objective : Lab number 2 works with a series LCR circuit. The purpose of the lab was to measure the generator output voltage by two methods. The first method used a multimeter, which gave the ε (rms) voltage. The second method gave the ε m voltage and it was measured with an oscilloscope. Afterwards we compared the two measurements. Method : ε (t)= ε m sin ϖ t ϖ =2 π f=1 / T Time Dependent Voltage: V R (t)=I(t)R V C (t)=I(t)X C V L (t)=I(t)X L X C =reactance of C=1/ ϖ C X L =reactance of L= ϖ L Amplitudes: V RM =I m R V CM =I m X C V LM =I m X L ε (rms)= ε m / √ 2 V R (rms)=V RM / √ 2 Kirchhoff’s Rule: V R (t)+V C (t)+V L (t)= ε (t) IR+(Q / C)+L(dI/dt)= ε m sin ϖ t L(d/dt)(dQ/dt)+R(dQ/dt)+(Q/C)= ε m sin ϖ t L(d 2 Q/dt 2 )+R(dQ/dt)+(Q/C)= ε m sin ϖ t Q=Q m sin( ϖ t-φ ) φ =phase of Q m Phase of Current I: I=dQ/dt=d/dt(Q m sin( ϖ t-φ ) = ϖ Q m cos( ϖ t-φ ) ϖ Q m =I m I=I m cos( ϖ t-φ ) I=I m sin( ϖ t- ( φ-π /2)) I=I m sin( ϖ t-φ ) Phase of V RM : V R =IR=I m sin( ϖ t-φ )R =I m Rsin( ϖ t-φ ) V R =V RM sin( ϖ t-φ ) Phase of V CM : V C =Q/C=(Q m /C)sin( ϖ t-φ ) V C =V CM sin[( ϖ t-φ )-π /2] Phase of V LM : V L =L(dI/dt)=L(dI/dt)(I m sin( ϖ t-φ )) =LI m ϖ cos( ϖ t-φ ) =I m (L ϖ )sin( π /2+ ϖ t-φ ) V L =V LM sin( π /2+ ϖ t-φ ) Phase of Q: Q=Q m sin( ϖ t-φ ) Q=Q m sin( ϖ t-φ-π /2) Impedance: z LCR = √ [(X L- X C ) 2 +R 2 ] z LCR = √ [(L ϖ- 1/ ϖ C)+R 2 ] Resonance in LCR: V RM =I m R I m = ε m / z LCR V RM = ε m R / z LCR V(rms)= ( ε / √ 2)(R/z LCR ) X L =X C L ϖ =1/ ϖ C ϖ = ϖ ϖ =1/ √ (LC) Energy and Power for LCR: U C (t)=instantaneous energy stored in C=Q 2 (t) / 2C U L (t)=instantaneous energy stored in L=LI 2 (t) / 2 P R (t)=power dissipated in R=I...
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Lab2 - Julia Bielaski 0163140 Lab Report#2 PH 327 Objective...

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