What do you mean by electrical resonance? An LC circuit is in a condition of resonance. If C=$1.0\times {{10}^{-6}}F$ and $L=0.25H$, then find the frequency of oscillation of the circuit.
Answer
Verified672k+ views
Hint: LC circuit is a closed loop circuit with two elements only and those are capacitor and an inductor. It does not have resistance in the circuit. It resonates at a natural frequency. Therefore it stores electrical energy.
Complete step by step solution:
Note: Frequency of oscillation of the LC circuit is dependent on capacitor and inductor only. It is independent of resistance. The frequency at which capacitive reactance and inductive reactance are same in magnitude and opposite in sign is called resonant frequency. Unit of frequency is Hz.
Complete step by step solution:
Electrical resonance: In A.C. circuit with inductor and capacitor, when the frequency of A.C is gradually changed at certain frequency, the impedance becomes minimum. This condition is called resonance and such a circuit is called a “resonant circuit”.
Circuit: A series combination of inductor of inductance L, capacitor of capacitance C connected with source of alternating e.m.f. forms a series LC circuit as shown below,
Formula of inductive reactance is,
${{X}_{L}}$$=2\pi fL$
Formula of capacitive reactance is,
${{X}_{C}}=\dfrac{1}{2\pi fC}$
At resonance, ${{X}_{L}}={{X}_{C}}$ -(1)
Put the value of capacitive reactance and inductive reactance in equation (1).
Therefore,
$2\pi fL=\dfrac{1}{2\pi fC}$
$2\pi {{f}^{2}}L=\dfrac{1}{2\pi C}$
Therefore,
${{f}^{2}}=\dfrac{1}{{{(2\pi )}^{2}}LC}$
$f=\dfrac{1}{2\pi \sqrt{LC}}$
Where, C = capacitor
L = inductor
Numerical: Given data-
C=$1.0\times {{10}^{-6}}F$and $L=0.25H$
We know that, frequency of oscillation of the LC circuit in resonance is given by,
$f=\dfrac{1}{2\pi \sqrt{LC}}$
$f=\dfrac{1}{2\pi \sqrt{1\times {{10}^{-6}}\times 0.25}}$
$f=318.3Hz$
Therefore, Frequency of oscillator of the LC circuit $f=318.3Hz$.
Recently Updated Pages
Which of the following graphs shows the variation of class 12 physics CBSE
Draw a labelled diagram of the human male reproductive class 12 biology CBSE
Describe the experiment to compare the emf of two cells class 12 physics CBSE
What is standard hydrogen electrode
What is conventional current and electric current class 12 physics CBSE
2Bromopentane is treated with an alcoholic KOH solution class 12 chemistry CBSE
Trending doubts
Draw a labelled sketch of the human eye class 12 physics CBSE
Which are the Top 10 Largest Countries of the World?
Differentiate between homogeneous and heterogeneous class 12 chemistry CBSE
Draw ray diagrams each showing i myopic eye and ii class 12 physics CBSE
Which is the correct genotypic ratio of mendel dihybrid class 12 biology CBSE
What is the Full Form of PVC, PET, HDPE, LDPE, PP and PS ?