R.ll*45 An RLC circuit such as that of Fig. 31-7 has R = Fig. 31-7 A single-loop circuit5.00 N, C = 20.0 µF, L = 1.00 H, and E = 30.0 V. (a) At containing a resistor, a capacitor,what angular frequency w, will the current amplitude have itsmaximum value, as in the resonance curves of Fig. 31-13? (b) resented by a sine wave in a circle,What is this maximum value? At what (c) lower angular fre- produces an alternating emf that es-quency w and (d) higher angular frequency wn will the cur-rent amplitude be half this maximum value? (e) What is directions of the emf and current(wn - wn)lw, the fractional half-width of the resonance curvefor this circuit? SSM wwwand an inductor. A generator, rep-tablishes an alternating current: theare indicated here at only one in-stant. R=10 2Fig. 31-13 Resonance curves for the driven RLC circuit of Fig. 31-7 withL = 100 µH, C = 100 pF, and three values of R. The current amplitude I ofthe alternating current depends on how close the driving angular frequencyw, is to the natural angular frequency w. The horizontal arrow on eachcurve measures the curve's half-width, which is the width at the half-maxi-mum level and is a measure of the sharpness of the resonance. To the leftof walw = 1.00, the circuit is mainly capacitive, with Xc > X; to the right,it is mainly inductive, with X > Xc.Xe > X,X > XcR= 30 2R= 10020.900.951.001.051.10Current amplitude /

Given In the series RLC circuit resistance of the resistor is R=5Ω the capacitance of the capacitor…

- 45 An RLC circuit such as that of Fig. 31-7 has R = 5.00 2. C 20.0 μF, L = 1.00 H. and 8, 30.0 V. (a) At what angular frequency o will the current amplitude have its maximum value, as in the resonance curves of Fig. 31-13? (b) What is this maximum value? At what (c) lower angular fre- quency and (d) higher angular frequency 2 will the cur- rent amplitude be half this maximum value? (e) What is (ww2)/0, the fractional half-width of the resonance curve for this circuit? SSM www 84 www R voo Fig. 31-7 A single-loop circuit containing a resistor, a capacitor, and an inductor. A generator, rep- resented by a sine wave in a circle. produces an alternating emf that es- tablishes an alternating current; the directions of the emf and current are indicated here at only one in- stant.

- 45 An RLC circuit such as that of Fig. 31-7 has R = 5.00 2. C 20.0 μF, L = 1.00 H. and 8, 30.0 V. (a) At what angular frequency o will the current amplitude have its maximum value, as in the resonance curves of Fig. 31-13? (b) What is this maximum value? At what (c) lower angular fre- quency and (d) higher angular frequency 2 will the cur- rent amplitude be half this maximum value? (e) What is (ww2)/0, the fractional half-width of the resonance curve for this circuit? SSM www 84 www R voo Fig. 31-7 A single-loop circuit containing a resistor, a capacitor, and an inductor. A generator, rep- resented by a sine wave in a circle. produces an alternating emf that es- tablishes an alternating current; the directions of the emf and current are indicated here at only one in- stant.