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## Explanation & Answer

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Name of the instructor

Section of the Lab

Name of the Student

Date Conducted: mm/dd/yy

# 19 Behavior of Resonance and RLC Circuits

Lab partners

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II. Introduction

RLC circuit can incorporate similar knowledge as that of RC in studying its response to

sinusoidal voltage. Majority of RLC circuits’ applications apply resonance frequencies as shown

in the figure.

The figure above has a source of sinusoidal voltage which brought the difference between part I

lab and this part II lab. The potential of sinusoidal voltage is given as:

VS=V0 Cos ωt where ω could be varied. From the above diagram, a difference occurs in that the

right side no longer appears to be zero in response to none applied voltage but V0 Cos ωt given

as:

𝑑2 𝑄

L 𝑑𝑡 2 +R

𝑑𝑄 1

+ Q= V0 Cos ωt

𝑑𝑡 𝐶

The solution to the function above is a result of change in time of charge Q of the capacitor.to get

the solution for the function, it assumed that the results is sinusoidal with similar frequency to

that of the driving voltage but has a phase difference given as:

Q=Q0 Cos (ωt+ϕ)

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Appropriate derivatives from the equation of sinusoidal voltage and the above expression are

used to determine Q0 and ϕ to make a solution. Cos (ωt+ϕ) and Sin (ωt+ϕ) functions are

expanded using sum formulas so that coefficients vanish when Sin ωt and Cos ωt are collected.

Solving the above functions yields these two equations:

𝑅

Tanϕ=𝜔𝐿−1/𝜔𝐶 Eq. 19.4&

Q0= -

𝑉0 𝑆𝑖𝑛 ϕ

𝜔𝑅

Eq. 19.5

The equation for Tanϕ indicates that its values are negative and very small at very low

frequencies such that ϕ is a negative and small angle while Sin ϕ≈0. Accor...