Download AC Circuit Experiment - Laboratory 10 Report | PH 106 and more Lab Reports Physics in PDF only on Docsity! Course and Section_______ Names ___________________________ Date___________ _________________________________ AC CIRCUIT EXPERIMENT This lab deals with circuits involving resistors, capacitors and inductors in which the currents and voltages vary sinusoidally in time. Equipment 1 function generator (PC Scope software) 1 digital multimeter and leads 1 decade resistance box 1 capacitor (nominally 0.1 µF) 1 inductor (nominally 10 mH) 1 mini-jack to banana plug (black, red, blue) cable, 2 alligator clips Introduction If the current through a passive component is given by )tfsin(I)tsin(I)t(i πω 2== . (1) then the voltage across the component also varies sinusoidally, but with a phase that depends on the component. For a resistor the voltage is in phase with the current. For a capacitor the voltage lags the current by 90o, and for an inductor the voltage leads the current by 90o. The peak (or rms) current-voltage relationships for a resistor, capacitor and inductor are (2) IRVR = )C/(IIXV CC ω== (3) LIIXV LL ω== (4) Series RC Circuit In a series RC circuit, since the currents are the same then the C voltages across R and C are 90o out of phase. R Consequently, the total voltage across the combination is 22 CXRIV += (5) v(t) = V sin(ω t+ϕ) Figure 1 R L Series RL Circuit In a series RL circuit, the voltages across R and L will also be 90o out of phase. Thus, 22 LXRIV += (6) v(t) = V sin(ω t+ϕ) Figure 2 Series RLC Circuit In a series RLC circuit, since the voltage across L leads the current by 90o and the voltage across C lags the current by 90o, then the voltages across L and C are 180o out of phase. Consequently, we have R C L ( )22 CL XXRIZ −+= . (7) We can write this as , where ZIV = ( )22 CL XXRZV −+== is the circuit impedance. In the series RLC circuit, the current will be a maximum when the impedance is a minimum, that is, when XL = XC, or LC ff π2 1 0 == (8) Preliminary Questions 1. In a series RC circuit, VR and VC are measured as a function of frequency. Do you expect VR and VC to increase, decrease, or remain constant as you change f? Show your predictions by making a sketch of VR and VC versus f. 2. In a series RL circuit the rms voltage across R is 30 V and the rms voltage across L is 40 V. What is the rms value of the voltage across the RL combination? 3. In a series RLC circuit, the rms voltage across L is 40 V and the rms voltage across C is 60 V. What is the rms voltage across the LC combination? v(t) = V sin(ω t+ϕ) Figure 3
