AC CIRCUIT LCR CIRCUIT LAB REPORT Table of Contents LCR CIRCUIT ................................................................................................................................ 2 Objectives ....................................................................................................................................... 2 Apparatus (virtual) .......................................................................................................................... 2 Introduction ..................................................................................................................................... 2 LCR capacitive circuit. ............................................................................................................... 3 LCR inductive circuit .................................................................................................................. 4 LCR series Resonance circuit ..................................................................................................... 4 Experimental data and observations ............................................................................................... 5 Experimental LCR circuit ............................................................................................................... 5 Calculations..................................................................................................................................... 6 Discussion and results ..................................................................................................................... 7 List of table and figures Table 1: Experimental data.......................................................................................................... 5 Figure 1:The phase angle relations of each LCR component with the voltage ....................... 3 Figure 2:The phases difference for LCR components with DC power source ........................ 3 Figure 3:The x and y-components of the phase difference across each component of LCR at the resonance ................................................................................................................................. 4 Figure 4:The circuit diagram of LCR circuit with alternating source AC ............................. 6 AC CIRCUIT LCR CIRCUIT LAB REPORT LCR CIRCUIT 1 Objectives ο· To build the LRC circuit via online simulations ο· To demonstrate and analyze the series LCR circuit with alternating voltage source With frequency π = 60π»π§ ο· To experimentally determine the resonance frequency of LCR circuit 2 Apparatus (virtual) This lab consists of series resonance circuit which have four components connected in series. ο· an inductor (L), ο· capacitor (C) and ο· resistor (R) ο· Alternating voltage source For this lab we used the simulations on the website. https://www.falstad.com/circuit/circuitjs.html 3 Introduction In a series RLC circuit containing a resistor, an inductor and a capacitor the source voltage is alternating. An LCR circuit is an electrical circuit consisting of a resistor (R), an inductor (L), and a capacitor (C), The formula for determining the resonant frequency of a series LCR circuit is: ππ = 1 2π√πΏπΆ An important property of this circuit is its ability to resonate at a specific frequency, The resonance π frequency (ππππ = 2π ). We have discussed here only the series combinations of LCR circuit components. AC CIRCUIT LCR CIRCUIT LAB REPORT The phase angle relation between the instantaneous voltage across each component ο· The instantaneous voltage across a pure resistor, VR is “in-phase” with current ο· The instantaneous voltage across a pure inductor, VL “leads” the current by 90o ο· The instantaneous voltage across a pure capacitor, VC “lags” the current by 90o ο· Therefore, VL and VC are 180o “out-of-phase” and in opposition to each other. Figure 1:The phase angle relations of each LCR component with the voltage Figure 2:The phases difference for LCR components with DC power source 3.1 LCR capacitive circuit. In the LCR capacitive circuit, the capacitive reactance is greater than the inductive reactance. AC CIRCUIT LCR CIRCUIT LAB REPORT XC > XL then the overall circuit reactance is capacitive giving a leading phase angle. 3.2 LCR inductive circuit Likewise, if the inductive reactance is greater than the capacitive reactance. XL > XC then the overall circuit reactance is inductive giving the series circuit a lagging phase angle. 3.3 LCR series Resonance circuit If the two reactance’s are the same and XL = XC then the angular frequency at which this occurs is called the resonant frequency and produces the effect of resonance. Figure 3:The x and y-components of the phase difference across each component of LCR at the resonance AC CIRCUIT LCR CIRCUIT LAB REPORT 4 Experimental data and observations Frequency of AC Resistance Inductance Resonance Resonance source frequency frequency (calculated) (measured) (Hz) (πΊ) (H) (Hz) (Hz) 60 10 1 41.1 41.01 Table 1: Experimental data 5 Experimental LCR circuit The following figure is experimentally built in the online simulations on the website; https://www.falstad.com/circuit/circuitjs.html AC CIRCUIT LCR CIRCUIT Figure 4:The circuit diagram of LCR circuit with alternating source AC 6 Calculations The reactance of a capacitor is defined as; ππ = 1/ππΆ For inductor ππΏ = ππΏ At the resonance ππΏ = ππΆ OR π2 = 1/πΏπΆ ππ = 1 2π√πΏπΆ LAB REPORT AC CIRCUIT LCR CIRCUIT ππ = LAB REPORT 1 2(3.1416)√1(15π −6 ππ = 41.1 π»π§ πππ. πππππ = | ππππ‘π’ππ − ππππππ’πππ‘ππ | . 100 ππππ‘π’ππ πππ. πππππ = | 41.01 − 41.1 | . 100 41.01 πππ. πππππ = 0.2% 7 Discussion and results The experimentally analyzed the resonance phenomenon, the resonance occurs because energy is stored in two different ways: in an electric field as the capacitor is charged and in field as current flows through the inductor connected in series or in parallel. the two reactance’s are the same and XL = XC then the angular frequency at which this occurs is called the resonant frequency and produces the effect of resonance. The circuit become resonant at the frequency which is 41.01 Hz. It is concluded that there was a 0.2% error in the actual and measured value for the resonance.