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...

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.