(a) Explanation Given data: The quality factor Q 0 is 7 . The value of the resistance R is 100 Ω . The value of the inductance L is 1.5 mH . Calculation: The conversion from krad / s to rad / s is given as, 1 krad / s = 10 3 rad / s The conversion of 90 krad / s into rad / s is given as, 90 krad / s = 90 × 10 3 rad / s = 90 × 10 3 rad / s Hence, angular frequency ω is, ω = 90 × 10 3 rad / s The conversion from mH to H is given by, 1 mH = 10 − 3 H The conversion of 1 .5 mH to H is given by, 1 .5 mH = 1.5 × 10 − 3 H Hence, the inductance L is, L = 1.5 × 10 − 3 H The quality factor Q 0 is given by, Q 0 = 1 R L C (1) Here, C is the capacitance. Substitute 100 Ω for R , 7 for Q 0 and 1.5 × 10 − 3 H for L in the above equation. 7 = 1 100 Ω 1.5 × 10 − 3 H C C = 1.5 × 10 − 3 ( 700 ) 2 = 3.06 × 10 − 9 F The quality factor is reduced to 5 by adjusting resistance R . Substitute 3.06 × 10 − 9 F for C , 5 for Q 0 and 1.5 × 10 − 3 H for L in equation (1). 5 = 1 R 1.5 × 10 − 3 H 3.06 × 10 − 9 F R = 1 5 490196 R = 140 Ω The impedance Z for series R L C circuit is given by, Z = R + j ω L + 1 j ω C (2) Here, ω is the angular frequency. The impedance Z at ω = 90 × 10 3 rad / s is given by, Substitute 140 Ω for R , 1.5 × 10 − 3 H for L , 3.06 × 10 − 9 F for C and 90 × 10 3 rad / s for ω in equation (2). Z = ( 140 Ω ) + j ( 90 × 10 3 rad / s ) ( 1.5 × 10 − 3 H ) + 1 j ( 90 × 10 3 rad / s ) ( 3.06 × 10 − 9 F ) = 140 + j 135 − j 3631 Ω = ( 140 − j 3496 ) Ω The estimated angle for the impedance θ est is given by, θ est = tan − 1 ( Im ( Z ) Re ( Z ) ) (3) Substitute − 3496 Ω for Im ( Z ) and 140 Ω for Re ( Z ) in the above equation (b) To determine The percent error in the estimated values compared to the exact values of angles.

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ISBN: 9781260540666

Author: Hayt

Publisher: MCG CUSTOM

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Chapter 15, Problem 35E

(a)

To determine

The angle of the impedance for the given condition.

(b)

To determine

The percent error in the estimated values compared to the exact values of angles.

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Chapter 15, Problem 34E

Chapter 15, Problem 36E

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The angle of the impedance for the given condition.

Solution Summary: The author explains the angle of the impedance for the given condition. The quality factor Q_0 is 7, the resistance 100Omega and the induct

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The angle of the impedance for the given condition.

The percent error in the estimated values compared to the exact values of angles.

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