If L and C in a parallel resonant circuit resonate at 1000 kHz and their product remains constant, what will be the resulting resonant frequency?

If L and C in a parallel resonant circuit resonate at 1000 kHz and their product remains constant, what will be the resulting resonant frequency?

• A. 10,000 kHz
• B. 100 kHz
• C. 1 MHz
• D. None of the above

Answer: (C)

In a parallel resonant circuit, the resonant frequency (f) can be calculated using the formula: \[ f = \frac{1}{2\pi\sqrt{LC}} \] where L is the inductance and C is the capacitance. When it is said that the product of L and C remains constant, it means that if one of these components is changed while the other is adjusted accordingly, their product (L * C) will hold the same value. Given that the original resonant frequency is 1000 kHz, if L and C maintain their product, any changes to either would affect the individual values of L or C but not their product. However, to achieve a resonant frequency of 1 MHz, corresponding values of L and C must be modified to fit the new frequency while keeping their product constant. To compute the desired frequency in the general case, if L and C are reduced appropriately, the new frequency can achieve a higher value while still satisfying the requirement for their product to remain unchanged. Consequently, reaching 1 MHz is achievable with suitable changes to the values of L and C that keep their product constant. Therefore, 1 MHz is the correct resonant frequency for these changes.

In a parallel resonant circuit, the resonant frequency (f) can be calculated using the formula:

[ f = \frac{1}{2\pi\sqrt{LC}} ]

where L is the inductance and C is the capacitance. When it is said that the product of L and C remains constant, it means that if one of these components is changed while the other is adjusted accordingly, their product (L * C) will hold the same value.

Given that the original resonant frequency is 1000 kHz, if L and C maintain their product, any changes to either would affect the individual values of L or C but not their product. However, to achieve a resonant frequency of 1 MHz, corresponding values of L and C must be modified to fit the new frequency while keeping their product constant.

To compute the desired frequency in the general case, if L and C are reduced appropriately, the new frequency can achieve a higher value while still satisfying the requirement for their product to remain unchanged.

Consequently, reaching 1 MHz is achievable with suitable changes to the values of L and C that keep their product constant. Therefore, 1 MHz is the correct resonant frequency for these changes.