The L-R-C Parallel Circuit. A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency ω . Let the source voltage be given by υ = V cos ω t. (a) Show that each of the instantaneous voltages υ R , υ L , and υ C at any instant is equal to u and that i = i R + i L + i C , where i is the current through the source and i R , i L , and i C are the currents through the resistor, inductor, and capacitor, respectively, (b) What are the phases of i R , i L , and i C with respect to υ ? Use current phasors to represent i , i R , i L , and i C. In a phasor diagram, show the phases of these four currents with respect to υ . (c) Use the phasor diagram of part (b) to show that the current amplitude I for the current i through the source is I = I R 2 + ( I C − I L ) 2 . (d) Show that the result of part (c) can be written as I = V / Z , with 1/ Z = ( 1 / R 2 ) + [ ω C − ( 1/ ω L ) ] 2 .
The L-R-C Parallel Circuit. A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency ω . Let the source voltage be given by υ = V cos ω t. (a) Show that each of the instantaneous voltages υ R , υ L , and υ C at any instant is equal to u and that i = i R + i L + i C , where i is the current through the source and i R , i L , and i C are the currents through the resistor, inductor, and capacitor, respectively, (b) What are the phases of i R , i L , and i C with respect to υ ? Use current phasors to represent i , i R , i L , and i C. In a phasor diagram, show the phases of these four currents with respect to υ . (c) Use the phasor diagram of part (b) to show that the current amplitude I for the current i through the source is I = I R 2 + ( I C − I L ) 2 . (d) Show that the result of part (c) can be written as I = V / Z , with 1/ Z = ( 1 / R 2 ) + [ ω C − ( 1/ ω L ) ] 2 .
The L-R-C Parallel Circuit. A resistor, an inductor, and a capacitor are connected in parallel to an ac source with voltage amplitude V and angular frequency ω. Let the source voltage be given by υ = Vcos ωt. (a) Show that each of the instantaneous voltages υR, υL, and υC at any instant is equal to u and that i = iR + iL + iC, where i is the current through the source and iR, iL, and iC are the currents through the resistor, inductor, and capacitor, respectively, (b) What are the phases of iR, iL, and iC with respect to υ? Use current phasors to represent i, iR, iL, and iC. In a phasor diagram, show the phases of these four currents with respect to υ. (c) Use the phasor diagram of part (b) to show that the current amplitude I for the current i through the source is
I
=
I
R
2
+
(
I
C
−
I
L
)
2
. (d) Show that the result of part (c) can be written as I = V/Z, with 1/Z =
(
1
/
R
2
)
+
[
ω
C
−
(
1/
ω
L
)
]
2
.
a cubic foot of argon at 20 degrees celsius is isentropically compressed from 1 atm to 425 KPa. What is the new temperature and density?
Calculate the variance of the calculated accelerations. The free fall height was 1753 mm. The measured release and catch times were:
222.22 800.00
61.11 641.67
0.00 588.89
11.11 588.89
8.33 588.89
11.11 588.89
5.56 586.11
2.78 583.33
Give in the answer window the calculated repeated experiment variance in m/s2.
Chapter 31 Solutions
University Physics with Modern Physics (14th Edition)
College Physics: A Strategic Approach (3rd Edition)
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