Question

In the figure bclow, a generator with an adustable frequency of oscillation is connected to resistance R 860 n ind tances L1 0 mH and L2 2 m a capac tances C 8 00니 C S a and -7.00 i (a) What is the resonant frequency of the circuit? Hz (b) What happens to the resonant frequency if R is increased? It increases It decreases It stays the same. (c) What happens to the resonant frequency it L1 is increased? O It increases. O It decreases It stays the same. (d) What happens to the resonant frequency if C3 is removed from the circuit? It increases t stays the same.

Answer 1

C_1, C_2, C_3 are in parallel converting the C_1, C_2, C_3 to a single capacitor C_eq - C_1 + C_2 + C_3 The inductors L_1, L_2 are in series L_1 + L_2 { lumping inductors} L_eq = L_1 + L_2 L_eq = 1.30 mH + 2.70 mH = 4mH C_eq = 8 MF + 5 MF + 7 MF = 20 MF \r\n C_eq The circuit will be in serier resonance: At resonance (f_r) = 1/2 pi squareroot LC = 1/2 pi squareroot L_eq C_eq = 1/2 pi squareroot (4 times 10^-3) times (20 times 10^-6) = 1/2 pi squareroot (80 times 10^-9) = 562.697 H_2 f_r = 1/2 pi squareroot LC: Even if the resistance is increased, it has no effect on resonance frequency. Therefore the resonance frequency remain constant: \r\n when L_1 is increased, L_eq = L_1 + L_2 Therefore increases: rightdoublearrow f_r = 1/2 pi squareroot L_eq C_eq