Reactance(X) and Resonance In an a.c circuit

Physics

Chima Sunday (Tutor)
18-02-2016 16:13:00 +0000

RESONANCE
In our last discussion, we handled Reactance of Capacitor and Inductor. Today we will be discusing on the subject of Resonance. Resonance is said to occur in physics when a body or system is made to vibrate at its natural frequency due to the influence of other vibrating body or system. In an a.c circuit, resonance frequency occur when inductive reactance equals to capacitive reactance. This happens in two occasions . One is when inductor L, capacitor C and resistor R are connected in series. Two is when inductor L, capacitor C and resistor R are connected in parallel. Here we are going to look at it when it is connected in series.
When these qauntities are connected in series, resonance is said to occur when the reactance of the inductor is equal to the reactance of capacitor
i.e X_L = X_c
so that 2πfl = ¹/_2πfl
by subject formular, f_o = ¹/_2π√(LC)
This gives the tuning frequency formular of our radio reciever. where f_o is the resonance frequency.
Example: An alternate current connected to an RLC series circuit has a peak value V_o. If the inductor is 0.5mH and capacitor 8microFarad. Determine the resonance frequency of the circuit.
solution
recall that resonance frequency is given by f_o = ¹/_2π√(LC)
from the question L = 0.5mH = 0.5×10^-3 and C = 8microfarad = 8×10^-6
∴ f_o = ¹⁄2π√(0.5)×10^-3 × 8×10^-6
i.e = ¹/&2π√4×10^-9 = ¹/&2π√40×10^-10
∴ f_o = ¹/2π× 6.3×10^-5
i.e = ¹/39.6×10^-5
f_o = 0.025×10⁵
i.e = 2500Hz = 2.5kHz

Can You
(1) If an inductive reactance of an inductor is is 15 ohms and capacitive reactance of the capacitor 100 ohms is connected in series to an a.c circuit of frequency 200Hz. Calculate the resonance frequency of the circuit. (take π = 3.142)
(2)The wavelength of Wazobia broadcasting station signal is 3m, If one which to listen to their programs with a tuning circuit of a radio receiver of inductor 50H. Calculate the value of the corresponding capacitor that can make it possible. (Hint take velocity of e.m waves = 3×10⁸ms^-1, frequency of broadcasting = resonance frequency and π = 3.142).
The tutor will be online tomorrow Friday 19th February, 2016 to answer all your questions. So leave your questions as a comment. CHEERS!