Question

I am currently trying to figure out the experiment below. Please complete Table 1 with an explanation, I appreciate it thank you!  Promise to give thumbs up!

Introduction The phase differences between the output voltage, the voltage across the inductor, the voltage across the capacitor, and the voltage across the resistor will be examined at resonant frequency. The voltage and phase relationship will also be examined for frequencies above and below resonance. Theory An inductor, a capacitor, and a resistor are connected in series with a sine wave generator as shown in figure 1. Since it is a series circuit, the current will be common to all the components and given by I = Imaxcos(wt) Equation 1 The voltage across the resistor will be in phase with the current, but the voltage across the inductor leads the current by 90° and the voltage across the capacitor lags by 90°. Adding the three EMF voltages, E, results in a total voltage that varies sinusoidally, but has a phase shift o with respect to the current and is given by E = Emaxcos(ot + o) Equation 2 The three components obey the AC analogs of Ohm's Law: Er =IR, EL max=ImaxXL, Ec max=ImaxXc, where XL and Xc are the AC analogs of resistance called the inductive reactance

Answer 1

here is the answer:-

$\phi$= 360 $\times$ (
Δt/T
) = 360 $\times$ ($\Delta t$)$\times f$ =

for resonance:-

$\phi$L = 360 $\times$ ($\Delta t$ VL)$\times f$ = 360 $\times$ (7.88$\times$10^-6)$\times$(30700) = 87.08

$\phi$C=360 $\times$ ($\Delta t$ VC)$\times f$ = 360 $\times$ (-7.81$\times$10^-6)$\times$(30700) = -86.31

$\phi$tot =360 $\times$ ($\Delta t$ Vo)$\times f$ = 360 $\times$ (0) $\times$ (30700) = 0

system	frequency	$\Delta t$ VL	$\Delta t$ VC	$\Delta t$ Vo	$\phi L$	$\phi C$	$\phi tot$
Resonance	30700	7.88	-7.81	0.00	87.08	-86.31	0
below resonance	18700	12.50	-12.80	-6.97	84.15	-86.16	-47.92
Above resonance	48700	5.10	-4.94	2.77	89.41	-86.61	48.56

please have a look that in $\phi$ tot do we have to make addition of $\phi$ L and $\phi$ C or we have to take $\Delta t$ Vo for calculations as taken here.

thank you.