1-6 X = X_{L}-X_{C}Suppose an a.c. circuit contains an X_{L} of 300 ohms and an X_{C} of 250 ohms. The resultant reactanceis: X = X_{L}-X_{C} = 300 -250 = 50 ohms (inductive) In some cases, the X_{C} may be larger than the X_{L}. If X_{L} = 1200 ohms and XC= 4000 ohms, the difference is: X = X_{L}-X_{C} = 1200 -4000 = -2800 ohms (capacitive). The total carries the sign (+ or -) of the greater number (factor). Q-1. What is the relationship between frequency and the values of (a) X_{L}, (b) X_{C}, and (c) R? Q-2. In an a.c. circuit that contains both an inductor and a capacitor, what term is used for the difference between the individual reactances? RESONANCEFor every combination of L and C, there is only ONE frequency (in both series and parallel circuits) that causes X_{L} to exactly equal X_{C}; this frequency is known as the RESONANT FREQUENCY. When the resonant frequency is fed to a series or parallel circuit, XLbecomes equal to X_{C}, and the circuit is said to be RESONANT to that frequency. The circuit is now called a RESONANT CIRCUIT; resonant circuits are tuned circuits. The circuit condition wherein X_{L} becomes equal to X_{C} is known as RESONANCE. Each LCR circuit responds to resonant frequency differently than it does to any other frequency. Because of this, an LCR circuit has the ability to separate frequencies. For example, suppose the TV or radio station you want to see or hear is broadcasting at the resonant frequency. The LC "tuner" in your set can divide the frequencies, picking out the resonant frequency and rejecting the other frequencies. Thus, the tuner selects the station you want and rejects all other stations. If you decide to select another station, you can change the frequency by tuning the resonant circuit to the desired frequency. RESONANT FREQUENCY As stated before, the frequency at which X_{L} equals X_{C} (in a given circuit) is known as the resonant frequency of that circuit. Based on this, the following formula has been derived to find the exact resonant frequency when the values of circuit components are known: There are two important points to remember about this formula. First, the resonant frequency found when using the formula will cause the reactances (X_{L} and X_{C}) of the L and C components to be equal. Second, any change in the value of either L or C will cause a change in the resonant frequency. An increase in the value of either L or C, or both L and C, will lower the resonant frequency of a given circuit. A decrease in the value of L or C, or both L and C, will raise the resonant frequency of a given circuit.

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