L-C-R Series and parallel Resonance

Transcription

1 Page o 6 L-C-R Series and parallel Resonance Aim :- To study the requency response and to ind resonant requencies o L-C-R series and parallel circuits. Also to ind the quality actor and band width in L-C-R series circuit. Apparatus :- A variable non-inductive resistor, a variable capacitor, a variable inductor, a signal generator, an a.c. milli- ammeter and the connecting wires. Formula :- The resonance requency = Hz 2π LC Where L = Sel inductance (mh) C = Capacity o the capacitor ( µf ) 2π Quality actor Q = R Where R = Resistance ( Ω ) Band width = ( 2 ) ( Hz ) Also Quality actor Q = L 2 Where and 2 are the requencies at the hal power points. Description and theory :- (Series L-C-R) When the resistor R, inductor L and capacitor C are connected in series with a source o em E, the circuit is called as the series resonant or series tuned circuit ( igure-). This is an acceptor circuit, that means it allows maximum current to low through it at a particular ( resonant ) requency and at all other requencies it allows less current. In A.C. circuits the voltage and the current are usually out o phase. Across the inductor, the current lags behind the voltage by 9, where as across the capacitor, the current leads the voltage by 9. But across the resistor the voltage and current both are in

2 Page 2 o 6 phase. Under certain conditions, the voltage and current are in phase, even though the circuit consists o L, C and R and the circuit behaves as a pure resistor. This phenomenon is called resonance. This occurs at a single requency known as resonant requency. At this requency the capacitive reactance( X c = /ωc) and the inductive reactance( X L = ωl) are equal and opposite in direction. So they get cancelled each other and only resistance acts. The impedance o the circuit is given by Z = R + j (ωl - /ωc ) At resonance the reactive term disappears ωl - /ωc = The impedance is minimum i.e. Z = R The current is maximum So ωl = /ωc I = E/R ω = ω = 2 π = LC At this requency the current is maximum and this requency is called resonant requency. The circuit has selective properties. To compare selectivity or sharpness o resonance, a band o requencies is chosen at which the current alls to times ( hal 2 power points ) o its maximum value. The requency dierence ( 2 ) between the hal power points is called the bandwidth. L-C-R parallel :- Parallel resonant circuit ( igure-2 ) is one in which one branch consists o an inductor L with associated resistor R and the other branch consists o a capacitor C. This is a rejector circuit, that means it rejects the current or allows minimum current to low through it, at a particular (anti- resonant ) requency and it allows more current at

3 Page 3 o 6 all other requencies. So the circuit is not selective. But it is highly selective when energized rom a high impedance generator. The impedance o the circuit is given by Z = + R + jω L jω C At resonance the impedance is maximum. The impedance at resonance Z = L CR The anti-resonance requency = 2 π R LC L o 2 2 Hz I R-value is small, then = Hz 2π LC Procedure :- For L-C-R series, the circuit is connected as shown in the igure-.the source resistance and the series resistance should be small. The out put voltage o the signal generator is adjusted to be around 5V. The requency o the signal generator is changed in steps and the corresponding current values are noted rom the a.c. milliammeter. The readings are tabulated. The current values increase with the increase o requency, up to the resonant requency, urther increase o requency causes the decrease o current. The L,C and R values are noted to calculate the resonant requency and Q- actor, using the above ormulae. Note :- The experiment may be repeated with a dierent values o R. Here the o value is un changed, but Q- actor value is changed.

4 Page 4 o 6 Graph :- A graph is drawn or current against requency. The requency corresponding to maximum current is noted and it is the resonant requency. The requencies and 2 corresponding to hal power points is noted and rom it the bandwidth, ( 2 ) is noted. From the values o, and 2, the quality actor, Q is calculated. For L-C-R parallel, the circuit is connected as shown in the igure-2. The requency o the signal generator is changed in steps and the corresponding current values are noted rom the a.c. milli- ammeter. The readings are tabulated. But here, the current values decrease with the increase o requency up to the anti- resonant requency, urther increase o requency causes the increase o current. The anti- resonant requency o is noted corresponding to the minimum current in the circuit. Graph :- A graph is drawn or current against requency. The requency corresponding to minimum current is noted and it is the anti- resonant requency. Precautions :- ) The internal resistance o the source and series resistance should be small. 2)Beore going to the experiment the resonant requency should be calculated rom L and C values so that to select the range o requencies or observation. Results :-

5 Page 5 o 6 Table- Table -2 L-C-R Series L-C-R Parallel S.No. Frequency (Hz) Current (ma) S.No. Frequency ( Hz ) Current ( ma ) 2. 2.

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