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

To build the LRC circuit via online simulations

To demonstrate and analyze the series LCR circuit with alternating voltage source
With frequency 𝑓 = 60𝐻𝑧

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.

an inductor (L),

capacitor (C) and

resistor (R)

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:
𝑓𝑟 =
1
2𝜋√𝐿𝐶
An important property of this circuit is its ability to resonate at a specific frequency, The resonance
𝜔
frequency (𝑓𝑟𝑒𝑠 = 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

The instantaneous voltage across a pure resistor, VR is “in-phase” with current

The instantaneous voltage across a pure inductor, VL “leads” the current by 90o

The instantaneous voltage across a pure capacitor, VC “lags” the current by 90o

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)
(𝛺)
(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;
𝑋𝑐 = 1/𝜔𝐶
For inductor
𝑋𝐿 = 𝜔𝐿
At the resonance
𝑋𝐿 = 𝑋𝐶
OR
𝜔2 = 1/𝐿𝐶
𝑓𝑟 =
1
2𝜋√𝐿𝐶
LAB REPORT
AC CIRCUIT
LCR CIRCUIT
𝑓𝑟 =
LAB REPORT
1
2(3.1416)√1(15𝑒 −6
𝑓𝑟 = 41.1 𝐻𝑧
𝑝𝑒𝑟. 𝑒𝑟𝑟𝑜𝑟 = |
𝑓𝑎𝑐𝑡𝑢𝑎𝑙 − 𝑓𝑐𝑎𝑙𝑐𝑢𝑙𝑎𝑡𝑒𝑑
| . 100
𝑓𝑎𝑐𝑡𝑢𝑎𝑙
𝑝𝑒𝑟. 𝑒𝑟𝑟𝑜𝑟 = |
41.01 − 41.1
| . 100
41.01
𝑝𝑒𝑟. 𝑒𝑟𝑟𝑜𝑟 = 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.