Test: AC Applied to LCR in Series

In a series RLC circuit there becomes a frequency point were the inductive reactance of the inductor becomes equal in value to the capacitive reactance of the capacitor. In other words, XL = XC.
Series Resonance circuits are one of the most important circuits used electrical and electronic circuits.
 

In an RLC circuit, the voltage is always used as a reference and according to the phase of the voltage, the phase of the other parameters is decided.

From the formula we get,
X_L=X_C
ωL=1/ωC
⇒ω²=1/LC
⇒ω=1/√Lc
⇒ω=1/√10^-3x10^-5
⇒ω=10⁴
We also know that,
X_L=ωL
⇒X_L=104x10-3
⇒X_L=10 Ω
Therefore,X_L=X_C=10Ω

Hotwire instruments are based on the heat I_rms²​Rt and/or power I_rms²​R producing property of current. Hence it can measure both ac and dc current as both produce heat when passed through a conductor.

Let’s keep this simple and to the point. We know that:
1.in a series circuit the same current flows through each component
2.the voltage across an ideal inductor L is 90˚ ahead of an AC current through it
3.the voltage across an ideal capacitor C is 90˚ behind an AC current through it
So putting these facts together we can conclude that given an AC series current the voltages across any L and C must have a phase difference of 180˚

Cosφ=R/Z=R/√R²/ ω²L²=5/√(25+(50)²x (0.1)²)
=5/√(25+25)=1/√2
⇒φ=π/4

In electrical engineering, admittance is a measure of how easily a circuit or device will allow a current to flow. It is defined as the reciprocal of impedance, analogous to how conductance & resistance are defined. The SI unit of admittance is the siemens (symbol S); the older, synonymous unit is mho, and its symbol is ℧ (an upside-down uppercase omega Ω). Oliver Heaviside coined the term admittance in December 1887. 
Admittance is defined as
Y=1/Z
where
Y is the admittance, measured in siemens
Z is the impedance, measured in ohms