North South University

• PHY 108

• 1. Objectives: 1) To understand the concept of resonance in simple RLC circuit. 2) To determine the resonance frequency in a parallel RLC circuit and compare this to the expected resonance value. 3) To understand concepts related to resonance such as bandwidth and Q- factor. 2. Background: Resonance is the tendency of a system to oscillate at maximum amplitude when excited at its natural frequency. Electrical resonance occurs when the impedance of part of the circuit reaches a maximum or a minimum at a particular frequency. This is called resonant frequency and its value depends on the circuit elements involved. The reactance of a capacitor is measured in ohms, is given by Xc= 1 2??? and the reactance of an inductor is measured in ohms, given by XL=2???. At low frequencies, the inductor caries most of the current because its impedance ZL = ??? is small. At high frequencies, the capacitor carries most of the current because its impedance ZC= 1 ??? , is small. At some point between, when |ZL| =|ZC|, you might expect that the inductor and the capacitor would each carry half the current. However, this is not the case because we are now dealing with vector quantities. For this condition there is in fact a resonance. The condition |ZL| =|ZC| can be written as ?? = 1 ?? or ? = 1 √?? and f= 1 2?√?? (1) So the expected resonance frequency is given by equation 1. f0= 1 2?√?? Quality Factor In RLC Circuit, the ratio of resonance frequency to the difference of its neighboring frequencies so that their corresponding signal is 1/√2 times of the peak value, is called Q-factor of the circuit. ∆? = ?2 − ?1 ? = ?0 ∆?