ECCE$2017$ Electric Circuit Analysis

Course Project

Design and simulate a series RLC sinusoidal resonant circuit

In this project, you will be designing a series RLC circuit, which resonates at a certain frequency. The value of resistor given to you is $1k$ and the resonant frequency is $3\mathrm{.}1831$ kHz $.$ Using the concept of resonance, choos the closest appropriate values of inductance $($ L $)$ and capacitance $($ C $)$ available in the lab $($see Tables $2$ and $3)$ so that the supply voltage $E=8V(p-p)$ and the voltage across L and C shouldn't exceed $16$ V $($p$-$p$)$ each. Thereafter, show your design work and justify why you are choosing a particular value of inductance and capacitance for this project.

Design Calculations

The chosen value of Inductance $L=q,$

because:

$q,$

$q,$

The chosen value of Capacitance $C=q,$

because: $q,$

$q,$

$q,$

Table $1.$ Available Resistances in the Lab

Model No$.$ RM$8$; RBB$6$; CR$-$B$/7$DC$0$

$\backslash$table$[[$R $(k),0\mathrm{.}0001,0\mathrm{.}001,0\mathrm{.}01,0\mathrm{.}1,1\mathrm{.}0,10\mathrm{.}0,100\mathrm{.}0],[$Rated Maximum Current $(mA),2200,700,220,70,22,7,2\mathrm{.}2]]$

Table $2.$ Available Inductances in the Lab

Model No$.$ L$40$

$\backslash$table$[[$L $(mH),1\mathrm{.}0,10\mathrm{.}0,100\mathrm{.}0,1000\mathrm{.}0],[$Rated Maximum Current $(mA),100,70,50,30]]$

Table $3.$ Available Capacitances in the Lab

Model No$.$ CD$11$; CC$-$B$/5$DC$1$

$\backslash$table$[[C(nF),$All Values$],[$Rated Maximum Voltage $($V$),200]]$

A$)$ Theoretical calculations

Consider the series RLC circuit given in Fig. $1.$ Calculate $x_{L_{+}}{x}_G,x_t,Z|,V_L,V_C||$ and $$ at each of the frequencies given in Table $4$ and complete the table.

Table $4$

$\backslash$table$[[$Parameters$,\backslash$table$[[f=1\mathrm{.}5kHz$