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An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes?
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An LC circuit consist of an capacity and a coil with a large number of...
Explanation:
An LC circuit is a resonant circuit that consists of an inductor and a capacitor. The resonant frequency of an LC circuit is given by the formula:
$f = \frac{1}{2\pi\sqrt{LC}}$
Where f is the resonant frequency, L is the inductance of the coil, and C is the capacitance of the capacitor.
Effect of increase in linear dimensions:
If all the linear dimensions of the elements of the circuit are increased by a factor of 2, the inductance of the coil and the capacitance of the capacitor will both increase by a factor of 2. The new values of L and C will be:
$L' = 2L$
$C' = 2C$
Effect on resonant frequency:
Substituting the new values of L and C in the formula for resonant frequency, we get:
$f' = \frac{1}{2\pi\sqrt{2L\cdot 2C}}$
Simplifying this expression, we get:
$f' = \frac{1}{2\pi\sqrt{4LC}}$
$f' = \frac{1}{2}\cdot\frac{1}{2\pi\sqrt{LC}}$
$f' = \frac{1}{2}f$
Therefore, if all the linear dimensions of the elements of the LC circuit are increased by a factor of 2, the resonant frequency of the circuit will decrease by a factor of 2.
An LC circuit is a resonant circuit that consists of an inductor and a capacitor. The resonant frequency of an LC circuit is given by the formula:
$f = \frac{1}{2\pi\sqrt{LC}}$
Where f is the resonant frequency, L is the inductance of the coil, and C is the capacitance of the capacitor.
Effect of increase in linear dimensions:
If all the linear dimensions of the elements of the circuit are increased by a factor of 2, the inductance of the coil and the capacitance of the capacitor will both increase by a factor of 2. The new values of L and C will be:
$L' = 2L$
$C' = 2C$
Effect on resonant frequency:
Substituting the new values of L and C in the formula for resonant frequency, we get:
$f' = \frac{1}{2\pi\sqrt{2L\cdot 2C}}$
Simplifying this expression, we get:
$f' = \frac{1}{2\pi\sqrt{4LC}}$
$f' = \frac{1}{2}\cdot\frac{1}{2\pi\sqrt{LC}}$
$f' = \frac{1}{2}f$
Therefore, if all the linear dimensions of the elements of the LC circuit are increased by a factor of 2, the resonant frequency of the circuit will decrease by a factor of 2.
Community Answer
An LC circuit consist of an capacity and a coil with a large number of...
Resonant frequency halves
both L & C are inversely proportional to length and directly proportional to their area
resonant frequency = 1/{2Π√[LC]}
areas quadruples as linear dimensions doubles
both L & C are inversely proportional to length and directly proportional to their area
resonant frequency = 1/{2Π√[LC]}
areas quadruples as linear dimensions doubles
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An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes?
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An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes?.
An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes? for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes? covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An LC circuit consist of an capacity and a coil with a large number of turns. Suppose if all the linear dimensions of all the elements of the circuit are increased by a factor of 2 while keeping the number of turns in coil constant. How does resonant frequency changes?.
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