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In a LCR-circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L to
- a)2L
- b)4L
- c)L/2
- d)L/4
Correct answer is option 'C'. Can you explain this answer?
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LCR-Circuit and Resonant Frequency
An LCR circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. When subjected to an alternating current (AC), the circuit exhibits resonance at a specific frequency known as the resonant frequency (f0). At the resonant frequency, the circuit impedance is at its minimum, and the circuit current is at its maximum.
Effect of Changing Capacitance
If the capacitance is changed from C to 2C, the resonant frequency of the circuit will shift. This can be determined by the formula:
f0 = 1/2π√(LC)
When capacitance is doubled, the resonant frequency will decrease by a factor of √2, given that the inductance remains constant.
Effect of Changing Inductance
To maintain the same resonant frequency, the inductance (L) of the circuit must be adjusted accordingly. The new inductance value (L') can be determined by the formula:
f0 = 1/2π√(L'C)
When capacitance is doubled and the resonant frequency remains unchanged, the inductance must be halved. This is because the capacitance has increased, resulting in a decrease in the frequency. To compensate for this decrease, the inductance must be reduced to maintain the same resonant frequency.
Answer
Therefore, the correct option is C, where the inductance should be changed from L to L/2, to keep the resonant frequency unchanged when capacitance is changed from C to 2C.
An LCR circuit consists of an inductor (L), a capacitor (C), and a resistor (R) connected in series. When subjected to an alternating current (AC), the circuit exhibits resonance at a specific frequency known as the resonant frequency (f0). At the resonant frequency, the circuit impedance is at its minimum, and the circuit current is at its maximum.
Effect of Changing Capacitance
If the capacitance is changed from C to 2C, the resonant frequency of the circuit will shift. This can be determined by the formula:
f0 = 1/2π√(LC)
When capacitance is doubled, the resonant frequency will decrease by a factor of √2, given that the inductance remains constant.
Effect of Changing Inductance
To maintain the same resonant frequency, the inductance (L) of the circuit must be adjusted accordingly. The new inductance value (L') can be determined by the formula:
f0 = 1/2π√(L'C)
When capacitance is doubled and the resonant frequency remains unchanged, the inductance must be halved. This is because the capacitance has increased, resulting in a decrease in the frequency. To compensate for this decrease, the inductance must be reduced to maintain the same resonant frequency.
Answer
Therefore, the correct option is C, where the inductance should be changed from L to L/2, to keep the resonant frequency unchanged when capacitance is changed from C to 2C.
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In a LCR-circuit, capacitance is changed from C to 2C. For the resonant frequency to remain unchanged, the inductance should be changed from L toa)2Lb)4Lc)L/2d)L/4Correct answer is option 'C'. Can you explain this answer?
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