Test: AC Applied to LCR in Series - JEE MCQ

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

Explanation:

- When XL > XC, the power factor is not equal to 1.
- The power factor is the ratio of the resistance (R) to the impedance (Z) in a circuit.
- When the inductive reactance (XL) is greater than the capacitive reactance (XC), the power factor is not equal to 1.
- This is because the presence of more inductive reactance causes the current to lag behind the voltage, leading to a phase difference.
- In such cases, the power factor is less than 1, indicating that the circuit is not purely resistive and has reactive components affecting the power flow.

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.

The correct answer is A.

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