The resonant frequency of an a.c circuit is 1000 kHz. If each of the capacitance and inductance in the circuit is reduced by 50%, and no other changes are m...
Question 1 Report
The resonant frequency of an a.c circuit is 1000 kHz. If each of the capacitance and inductance in the circuit is reduced by 50%, and no other changes are made, the resonant frequency will become
Answer Details
The resonant frequency of an a.c circuit is given by the formula:
f = 1/(2π√(LC))
Where f is the resonant frequency, L is the inductance of the circuit, and C is the capacitance of the circuit.
If each of the capacitance and inductance in the circuit is reduced by 50%, then the new values of L and C will be 0.5L and 0.5C respectively.
Substituting these new values into the formula, we get:
f' = 1/(2π√(0.5L * 0.5C))
f' = 1/(2π√(0.25LC))
f' = 1/(0.5π√(LC))
f' = 2f
Therefore, the resonant frequency of the circuit will be doubled, which means it will become 2000kHz.
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