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

Angel24579

2 years ago

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

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


250kHz

750kHz

1000kHz

2000kHz
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.
(solution from green bridge cbt)