Series and Parallel Resonant Circuits
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1 Seies and Paallel Resonant icuits OBJETIVE To detemine the esonant fequency, self-inductance and the quality facto of the coil in the seies and paallel cicuits. PRINIPE A coil of self-inductance is connected in seies with a capacitance and a esistance R. This cicuit is called as a seies R cicuit. If V i is the diving voltage a cuent, I will flow in the cicuit. At an angula fequency ω 0 of the ac souce, the cuent. I will be in phase with the voltage V. This condition is called as esonance and the cicuit is efeed to as a Seies Resonant icuit. If the inductance is connected in paallel with a capacitance and a esistance R, the cicuit is called as a paallel R cicuit. SPEIFI REQUIREMENT 2π Audio fequency oscillato, inductance coil, capacitance box, esistance box, milliammete, multimete. Fomulae. ω 0 = 2. = f = 2 π π 3. Q = ω 0 4. Q = whee ω 0 is the angula fequency is hetz. is the inductance of the coil in Heny. is the capacitance of the capacito is mico faad. R is the esistance of the esisto in ohm. is the esonant fequency of the seies o paallel esonant cicuit in hetz.
2 2 aboatoy Manual in Applied Physics PROEDURE Q is the quality facto of the coil. is the esistance of the coil in ohm. Seies Resonant icuit (a) The capacitance (), inductance (), esistance (R) and a milliammete (ma) ae connected in seies with an AFO as shown in the diagam. (b) The capacitance () is set to be 0. μf and esistance (R) is set as 50 ohms. (c) The audio fequency oscillato is adjusted to a minimum value of khz. (d) The cuent shown by milliammete is noted. (e) Keeping the and R values as a constant, the fequency of AFO is inceased in steps of 500 Hz and the coesponding milliammete eadings ae noted. (f) The same pocedue is epeated fo R = 00, R = 50 and R = 200 ohms, fo the same ange of fequency and the eadings ae tabulated. (g) A gaph is dawn with fequency along the X-axis and the cuent along the Y-axis. The fequency at which the cuent is maximum is the esonant fequency. Diagam : AFO ma Seies esonant cicuit. R Gaph : Y uent (ma) Fequency (Hz) X
3 Seies and Paallel Resonant icuits 3 TABE.: To detemine esonant fequency in seies mode apacitance () = µf (Resistance R = Ω) S.No. Fequency uent (Hz) (ma) PROEDURE PARAE RESONANT IRUIT (a) The inductance (), the esistance (R), ae connected in seies, and this is connected in paallel to the capacito (). (b) The milliammete (ma) and AFO ae connected as shown in diagam 2. Diagam 2: AFO ma R (c) The capacitance () is set to be 0. μf and the esistance (R) is set to be 50 ohms. (d) The audio fequency oscillato is adjusted fo a minimum value of f = khz. (e) The cuent in the cicuit shown by the milliammete is noted. (f) Keeping the and R values to be constant, the fequency is inceased in steps of 500 Hz and the milliammete eadings ae noted. (g) The esistance of the inductance coil () is measued using a multimete. (h) The pocedue is epeated fo R values of 00, 50 and 200 ohms fo the same ange of fequency and eadings ae tabulated. (i) A gaph is dawn with the fequency along the X-axis and the cuent along the Y-axis. The fequency at which the cuent is minimum is the esonant fequency. TABE.2: Paallel esonant cicuit to detemine the esonant fequency apacitance () = µf Resistance (R) = Ω S.No. Fequency uent (Hz) (ma)
4 4 aboatoy Manual in Applied Physics Gaph 2: Y uent (ma) Fequency (Hz) X AUATION Seies Resonant icuit (a) Resonant fequency fom gaph () is found to be =... Hz. (b) = f 2 R 2 4π f is the capacitance set is μf. =... milli Heny. (c) Quality facto of coil Q = 2 π f 2 R 4π fr. whee is the esistance, and it is pactically the esistance of the inductance coil and is measued using a multimete. AUATION Paallel Resonant icuit (a) The esonant fequency is noted fom the gaph is Hetz. 2 (b) = milli Heny whee is the capacitance set in mico faads. 2 (c) Q = 2 πfr whee is the esistance of the inductance coil and is measued using a multimete. RESUT Fo a Seies Resonant icuit. The esonant fequency is... Hz.
5 Seies and Paallel Resonant icuits 5 2. The inductance of the coil was found to be =... mh. 3. Quality facto was calculated to be Q =.... Fo a Paallel Resonant icuit. The esonant fequency =... Hz. 2. The inductance of the coil was found to be =... mh. 3. Quality facto was calculated to be Q =....
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