Answer
Verified
406.5k+ views
Hint: Students can use the dimensional analysis to compare the results in both the columns. The physical meaning of the terms in $\text{Column I}$can also be taken into consideration in order to find their formulae in $\text{Column II}$.
Complete step by step answer:
In order to match the above columns let us first take a look into the meaning or definition of the terms given in $\text{Column I}$ and then compare them with those given in $\text{Column II}$.
Definitions:
(i) Resonant frequency: Resonance is the phenomenon of increase of the amplitude of oscillation of a particular system. This increase in amplitude to the highest degree occurs at a particular frequency, which is known as the resonant frequency.
If ${{f}_{0}}$ is the resonant frequency of a system, then
${{f}_{0}}=\dfrac{1}{\sqrt{LC}}$
(ii) Quality factor: Quality factor in an LCR circuit is the ratio of the resonant frequency to the difference in two frequencies taken on both sides of the resonant frequency such that at each frequency, the current amplitude becomes $\dfrac{1}{\sqrt{2}}$ times the value at resonant frequency.
If $Q$ represents the quality factor of an LCR circuit, then
$Q=\dfrac{{{\omega }_{0}}L}{R}$
where, ${{\omega }_{0}}$ is the resonant frequency
$L$ is the self- inductance and
$R$ is the resistance of the circuit.
(iii) Average power: In an LCR circuit, if ${{P}_{av}}$ represents the average power of the circuit, then,
$\begin{align}
& {{P}_{av}}=\text{virtual emf}\times \text{virtual current}\times \cos \phi \\
& \Rightarrow {{P}_{av}}=V\times I\times \cos \phi \\
\end{align}$
where, $\cos \phi $ is known as the power factor.
(iv) Impedance: The effective resistance in the LCR circuit which opposes the flow of current through it is known as impedance.
$Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}$
Where, $Z$ is the impedance, $R$ is the resistance, ${{X}_{L}}$ is the inductive reactance and ${{X}_{C}}$ is the capacitive reactance of the circuit.
(v) Magnetic potential energy: The energy stored in a magnetic field induced in an inductor is equal to the work required to produce a current across the inductor.
If $M$ represents the magnetic potential energy across an inductor circuit, and $I$ represents the current through the circuit then,
$M=\dfrac{1}{2}L{{I}^{2}}$
(vi) Coefficient of self induction: Self-inductance of a coil is numerically equal to the change in the magnetic flux linked with the coil when unit current passes through it.
If $L$ is the coefficient of self induction or self inductance, then,
$L=\dfrac{E}{(\dfrac{dI}{dt})}$
where, $E$is the emf of the circuit and $\dfrac{dI}{dt}$ is the change in current across the circuit.
Therefore, the answer is option $A)a\to iii,b\to v,c\to i,d\to iv,e\to vi,f\to ii$.
Note: The option for resonant frequency given in the question is in $rad/s$ , that is, it is the angular resonant frequency. In case of frequency, a term $2\pi $ should have appeared in the denominator.
Complete step by step answer:
In order to match the above columns let us first take a look into the meaning or definition of the terms given in $\text{Column I}$ and then compare them with those given in $\text{Column II}$.
Definitions:
(i) Resonant frequency: Resonance is the phenomenon of increase of the amplitude of oscillation of a particular system. This increase in amplitude to the highest degree occurs at a particular frequency, which is known as the resonant frequency.
If ${{f}_{0}}$ is the resonant frequency of a system, then
${{f}_{0}}=\dfrac{1}{\sqrt{LC}}$
(ii) Quality factor: Quality factor in an LCR circuit is the ratio of the resonant frequency to the difference in two frequencies taken on both sides of the resonant frequency such that at each frequency, the current amplitude becomes $\dfrac{1}{\sqrt{2}}$ times the value at resonant frequency.
If $Q$ represents the quality factor of an LCR circuit, then
$Q=\dfrac{{{\omega }_{0}}L}{R}$
where, ${{\omega }_{0}}$ is the resonant frequency
$L$ is the self- inductance and
$R$ is the resistance of the circuit.
(iii) Average power: In an LCR circuit, if ${{P}_{av}}$ represents the average power of the circuit, then,
$\begin{align}
& {{P}_{av}}=\text{virtual emf}\times \text{virtual current}\times \cos \phi \\
& \Rightarrow {{P}_{av}}=V\times I\times \cos \phi \\
\end{align}$
where, $\cos \phi $ is known as the power factor.
(iv) Impedance: The effective resistance in the LCR circuit which opposes the flow of current through it is known as impedance.
$Z=\sqrt{{{R}^{2}}+{{({{X}_{L}}-{{X}_{C}})}^{2}}}$
Where, $Z$ is the impedance, $R$ is the resistance, ${{X}_{L}}$ is the inductive reactance and ${{X}_{C}}$ is the capacitive reactance of the circuit.
(v) Magnetic potential energy: The energy stored in a magnetic field induced in an inductor is equal to the work required to produce a current across the inductor.
If $M$ represents the magnetic potential energy across an inductor circuit, and $I$ represents the current through the circuit then,
$M=\dfrac{1}{2}L{{I}^{2}}$
(vi) Coefficient of self induction: Self-inductance of a coil is numerically equal to the change in the magnetic flux linked with the coil when unit current passes through it.
If $L$ is the coefficient of self induction or self inductance, then,
$L=\dfrac{E}{(\dfrac{dI}{dt})}$
where, $E$is the emf of the circuit and $\dfrac{dI}{dt}$ is the change in current across the circuit.
Therefore, the answer is option $A)a\to iii,b\to v,c\to i,d\to iv,e\to vi,f\to ii$.
Note: The option for resonant frequency given in the question is in $rad/s$ , that is, it is the angular resonant frequency. In case of frequency, a term $2\pi $ should have appeared in the denominator.
Recently Updated Pages
Basicity of sulphurous acid and sulphuric acid are
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
Three beakers labelled as A B and C each containing 25 mL of water were taken A small amount of NaOH anhydrous CuSO4 and NaCl were added to the beakers A B and C respectively It was observed that there was an increase in the temperature of the solutions contained in beakers A and B whereas in case of beaker C the temperature of the solution falls Which one of the following statements isarecorrect i In beakers A and B exothermic process has occurred ii In beakers A and B endothermic process has occurred iii In beaker C exothermic process has occurred iv In beaker C endothermic process has occurred
The branch of science which deals with nature and natural class 10 physics CBSE
What is the stopping potential when the metal with class 12 physics JEE_Main
The momentum of a photon is 2 times 10 16gm cmsec Its class 12 physics JEE_Main
Trending doubts
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
What is BLO What is the full form of BLO class 8 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
What organs are located on the left side of your body class 11 biology CBSE
The cell wall of prokaryotes are made up of a Cellulose class 9 biology CBSE
Select the word that is correctly spelled a Twelveth class 10 english CBSE
a Tabulate the differences in the characteristics of class 12 chemistry CBSE