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Can you explain the answer of this question below:
In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L to
- A:4L
- B:2L
- C:L/2
- D:L/4
The answer is d.
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**Explanation:**
To understand why the correct answer is option D (L/4), we need to analyze the behavior of an LCR circuit and the relationship between the inductance (L), capacitance (C), and resonant frequency.
**LCR Circuit:**
An LCR circuit consists of an inductor (L), capacitor (C), and resistor (R) connected in series or parallel. When an alternating current (AC) is applied to the circuit, it creates a resonant frequency at which the circuit exhibits maximum impedance.
**Resonant Frequency:**
The resonant frequency (f) of an LCR circuit is given by the formula:
f = 1 / (2 * π * √(LC))
where π is a constant (approximately 3.14159), and √(LC) represents the square root of the product of inductance (L) and capacitance (C).
**Effect of Changing Capacitance:**
When the capacitance (C) in an LCR circuit changes from C to 4C, the resonant frequency (f) remains the same. This means that the value of √(LC) must also remain constant.
Since the capacitance increases by a factor of 4, the square root of LC must decrease by a factor of 2 to maintain the same value. Therefore, the product of inductance (L) and capacitance (C) must decrease by a factor of 4.
**Effect on Inductance:**
To compensate for the increase in capacitance, the inductance (L) must decrease by a factor of 4 to maintain the same resonant frequency.
Therefore, the correct answer is option D (L/4), indicating that the inductance should be changed from L to L/4 when the capacitance is changed from C to 4C in an LCR circuit to maintain the same resonant frequency.
To understand why the correct answer is option D (L/4), we need to analyze the behavior of an LCR circuit and the relationship between the inductance (L), capacitance (C), and resonant frequency.
**LCR Circuit:**
An LCR circuit consists of an inductor (L), capacitor (C), and resistor (R) connected in series or parallel. When an alternating current (AC) is applied to the circuit, it creates a resonant frequency at which the circuit exhibits maximum impedance.
**Resonant Frequency:**
The resonant frequency (f) of an LCR circuit is given by the formula:
f = 1 / (2 * π * √(LC))
where π is a constant (approximately 3.14159), and √(LC) represents the square root of the product of inductance (L) and capacitance (C).
**Effect of Changing Capacitance:**
When the capacitance (C) in an LCR circuit changes from C to 4C, the resonant frequency (f) remains the same. This means that the value of √(LC) must also remain constant.
Since the capacitance increases by a factor of 4, the square root of LC must decrease by a factor of 2 to maintain the same value. Therefore, the product of inductance (L) and capacitance (C) must decrease by a factor of 4.
**Effect on Inductance:**
To compensate for the increase in capacitance, the inductance (L) must decrease by a factor of 4 to maintain the same resonant frequency.
Therefore, the correct answer is option D (L/4), indicating that the inductance should be changed from L to L/4 when the capacitance is changed from C to 4C in an LCR circuit to maintain the same resonant frequency.
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Can you explain the answer of this question below:In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L toA: 4L B: 2L C: L/2 D: L/4 The answer is d. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below:In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L toA: 4L B: 2L C: L/2 D: L/4 The answer is d. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L toA: 4L B: 2L C: L/2 D: L/4 The answer is d..
Can you explain the answer of this question below:In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L toA: 4L B: 2L C: L/2 D: L/4 The answer is d. for JEE 2025 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Can you explain the answer of this question below:In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L toA: 4L B: 2L C: L/2 D: L/4 The answer is d. covers all topics & solutions for JEE 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Can you explain the answer of this question below:In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L toA: 4L B: 2L C: L/2 D: L/4 The answer is d..
Solutions for Can you explain the answer of this question below:In LCR circuit, the capacitance is changed from C to 4C. For the same resonant frequency the inductance should be changed from L toA: 4L B: 2L C: L/2 D: L/4 The answer is d. in English & in Hindi are available as part of our courses for JEE.
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