Question

In the non-resonant circuit, what will be the nature of the circuit for frequencies higher than the resonant frequency?
A) Resistive
B) Capacitive
C) Inductive
D) None of these.

Answer 1

Hint:There are various conditions for the circuit to be resistive, capacitive and inductive. In ${X_L}$−${X_C}$which is inductive give $\omega L$−$\dfrac{1}{{\omega C}}$ here $\omega $ is the frequency,${X_L}$ is the inductive reactance and ${X_C}$ is the capacitive reactance. If $\omega $tends to smaller then $\dfrac{1}{{\omega C}}$becomes larger and vice versa

Step by step solution:
Step 1:
Resonant frequency is the oscillation of a system at its natural or unforced resonance. Resonance occurs when a system is able to store and easily transfer energy between different storage modes, such as Kinetic energy or Potential energy as you would find with a simple pendulum
The formula for impedance is ${Z^2}$ =${R^2}$ +${\left( {{X_L} - {X_C}} \right)^2}$ where, ${X_L}$ is the inductive reactance and ${X_C}$ is the capacitive reactance and R is the resistance.
Then suppose if our circuit becomes ${X_L}$−${X_C}$=0 then our circuit will be resistive.
Similarly, if ${X_L}$>${X_C}$, then circuit will be inductive
And if ${X_C}$ >${X_L}$, then it will be called a capacitive circuit.
Which means ${X_C}$and ${X_L}$only depends on frequency then in resonant condition our circuit will be resistive. That means option (1) is wrong
Now, ${X_L}$can be written as =$\omega L$ and ${X_C}$=$\dfrac{1}{{\omega C}}$
So in ${X_L}$−${X_C}$which is inductive give $\omega L$−$\dfrac{1}{{\omega C}}$ here $\omega $ is the frequency
If $\omega $tends to smaller then $\dfrac{1}{{\omega C}}$becomes larger, that means circuit will be of capacitive nature
And when it tends to be larger than the circuit be of inductive nature.
This is what was asked in the question. Inductive will be the nature of the circuit for frequencies higher than the resonant frequency

So option C is correct.

Note:Conditions for resonance: The resonance of a series RLC circuit occurs when the inductive and capacitive reactance is equal in magnitude but cancel each other because they are 180 degrees apart in phase. The sharp minimum in impedance which occurs is useful in tuning applications.