- #1

Michael 37

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## Homework Statement

The ac circuit has 3 components in series: a Capacitor C=120μF, an Inductor L=100mH, and a resistor R=7Ω.

A) Find the amplitude of the voltage across the resistor R in the LCR circuit below, when

operated at a frequency of 45 Hz?

B) What is the phase difference between this voltage and

the supply voltage, Vac (= (15 V)cosωt)?

C) At what frequency is this phase difference zero?

D)What is the Q value of this resonant circuit?

## Homework Equations

V(t)=Vocos(ωt + ∅)

Z=Vo/Io=R (Z=impedance)

ω=2πf

Q=(ωo)(L)/R

There the only relatable I can find

## The Attempt at a Solution

Attempt for part (A) Using V(t)=Vocos(ωt + ∅) I tried searching for Vo as that is the amplitude but we are not given any Voltage? Then I tried using Z=Vo/Io and I found the impedance but then I realized I don't have Io (current). So I was stuck plugging in numbers and trying to manipulate formulae to no avail.

Attempt for part (B) Well I think the voltage amplitude here is 15V with no phase change as ∅ is not present. So I said there is no difference as they must be in phase if there doesn't exist a ∅. Not sure if that is right.

Attempt for part (C) I used Q=(ωo)(L)/R, then I used the fact that ω=2πf which yielded an equation of the form Q=(2π)(f)(L)/R . I plugged in the figures and got a value of 4.04.

Please help! I am very stuck.