General Physics, 2nd Edition
General Physics, 2nd Edition
2nd Edition
ISBN: 9780471522782
Author: Morton M. Sternheim
Publisher: WILEY
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Chapter 20, Problem 82E

(a)

To determine

The value of ω for greatest current.

(a)

Expert Solution
Check Mark

Answer to Problem 82E

The value of ω for the greatest current is 103rad/s.

Explanation of Solution

Write the expression of ω for greatest current for a RLC circuit.

    ω=1LC        (1)

Here, ω is the resonant frequency, L is the inductance and R is the resistance.

Conclusion:

Substitute 0.01H for L and 104F for C in equation (1).

    ω=1(0.01H)(104F)=103rad/s

Thus, the value of ω for the greatest current is 103rad/s.

(b)

To determine

The magnitude of the frequency.

(b)

Expert Solution
Check Mark

Answer to Problem 82E

The corresponding frequency is 1570.8Hz.

Explanation of Solution

Write the expression for the frequency for a series RLC circuit.

    f=ω2π        (2)

Here, f is corresponding frequency.

Conclusion:

Substitute 103rad/s for ω in equation (2).

    f=103rad/s2π=1570.8Hz

Thus, the corresponding frequency is 1570.8Hz.

(c)

To determine

The power that is dissipated at the frequency.

(c)

Expert Solution
Check Mark

Answer to Problem 82E

The power dissipated is 20W.

Explanation of Solution

Write the expression for the impedance of a series RLC circuit.

    Z=R2+(XLXC)2        (3)

Here, Z is the impedance of the circuit, R is the resistance, XL inductive impedance and XC is capacitive impedance.

Write the expression for inductive impedance.

    XL=ωL        (4)

Write the expression for capacitive impedance.

    XC=1ωC        (5)

Write the expression for rms value of current.

    ie=veZ        (6)

Here, ie is the rms current and ve is the supply voltage.

Write the expression for the power dissipation in the circuit.

    P=ieve(RZ)        (7)

Here, P is the power.

Conclusion:

Substitute 0.01H for L and 103rad/s for ω in equation (4).

    XL=(0.01H)(103rad/s)=10ohm

Substitute 104F for C and 103rad/s for ω in equation (5).

    XC=1(104F)(103rad/s)=10ohm

Substitute 5ohm for R, 10ohm for XL and 10ohm for XC in equation (3)

    Z=(5ohm)2+(10ohm10ohm)2=5ohm

Substitute 5ohm for Z and 10V for ve in equation (6).

    ie=10V5ohm=2A

Substitute 2A for ie, 10V for ve, 5ohm for R and 5ohm for Z.

    P=(2A)(10V)(5ohm5ohm)=20W

Thus, the power dissipated is 20W.

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Chapter 20 Solutions

General Physics, 2nd Edition

Ch. 20 - Prob. 11RQCh. 20 - Prob. 12RQCh. 20 - Prob. 13RQCh. 20 - Prob. 1ECh. 20 - Prob. 2ECh. 20 - Prob. 3ECh. 20 - Prob. 4ECh. 20 - Prob. 5ECh. 20 - Prob. 6ECh. 20 - Prob. 7ECh. 20 - Prob. 8ECh. 20 - Prob. 9ECh. 20 - Prob. 10ECh. 20 - Prob. 11ECh. 20 - Prob. 12ECh. 20 - Prob. 13ECh. 20 - Prob. 14ECh. 20 - Prob. 15ECh. 20 - Prob. 16ECh. 20 - Prob. 17ECh. 20 - Prob. 18ECh. 20 - Prob. 19ECh. 20 - Prob. 20ECh. 20 - Prob. 21ECh. 20 - Prob. 22ECh. 20 - Prob. 23ECh. 20 - Prob. 24ECh. 20 - Prob. 25ECh. 20 - Prob. 26ECh. 20 - Prob. 27ECh. 20 - Prob. 28ECh. 20 - Prob. 29ECh. 20 - Prob. 30ECh. 20 - Prob. 31ECh. 20 - Prob. 32ECh. 20 - Prob. 33ECh. 20 - Prob. 34ECh. 20 - Prob. 35ECh. 20 - Prob. 36ECh. 20 - Prob. 37ECh. 20 - Prob. 38ECh. 20 - Prob. 39ECh. 20 - Prob. 40ECh. 20 - Prob. 41ECh. 20 - Prob. 42ECh. 20 - Prob. 43ECh. 20 - Prob. 44ECh. 20 - Prob. 45ECh. 20 - Prob. 46ECh. 20 - Prob. 47ECh. 20 - Prob. 48ECh. 20 - Prob. 49ECh. 20 - Prob. 50ECh. 20 - Prob. 51ECh. 20 - Prob. 52ECh. 20 - Prob. 53ECh. 20 - Prob. 54ECh. 20 - Prob. 55ECh. 20 - Prob. 56ECh. 20 - Prob. 57ECh. 20 - Prob. 58ECh. 20 - Prob. 59ECh. 20 - Prob. 60ECh. 20 - Prob. 61ECh. 20 - Prob. 62ECh. 20 - Prob. 63ECh. 20 - Prob. 64ECh. 20 - Prob. 65ECh. 20 - Prob. 66ECh. 20 - Prob. 67ECh. 20 - Prob. 68ECh. 20 - Prob. 69ECh. 20 - Prob. 70ECh. 20 - Prob. 71ECh. 20 - Prob. 72ECh. 20 - Prob. 73ECh. 20 - Prob. 74ECh. 20 - Prob. 75ECh. 20 - Prob. 76ECh. 20 - Prob. 77ECh. 20 - Prob. 78ECh. 20 - Prob. 79ECh. 20 - Prob. 80ECh. 20 - Prob. 81ECh. 20 - Prob. 82ECh. 20 - Prob. 83ECh. 20 - Prob. 84ECh. 20 - Prob. 85ECh. 20 - Prob. 86ECh. 20 - Prob. 87ECh. 20 - Prob. 88ECh. 20 - Prob. 89ECh. 20 - Prob. 90ECh. 20 - Prob. 91ECh. 20 - Prob. 92ECh. 20 - Prob. 93ECh. 20 - Prob. 94ECh. 20 - Prob. 95E
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