Voltage The electrical voltage from a standard wall outlet is given as a function of time t by V(t) = 170 sin(120 mt). This is an example of alternating current, which is electric- ity that reverses direction at regular intervals. The common method for measuring the level of voltage from an alternating current is the root mean square, which is given by Root mean square = P (1);^"S| T where T is one period of the current. (a) Verify that T = 1/60 second for V(t) given above. (b) You may have seen that the voltage from a standard wall outlet is 120 volts. Verify that this is the root mean square value for V(t) given above. (Hìnt: Use the trigo- nometric identity sin? x = (1 – cos 2x)/2. This identity can be derived by letting y = x in the basic identity for cos(x + y), and then eliminating cos? x by using the iden- tity cos x = 1 - sin x.)
Voltage The electrical voltage from a standard wall outlet is given as a function of time t by V(t) = 170 sin(120 mt). This is an example of alternating current, which is electric- ity that reverses direction at regular intervals. The common method for measuring the level of voltage from an alternating current is the root mean square, which is given by Root mean square = P (1);^"S| T where T is one period of the current. (a) Verify that T = 1/60 second for V(t) given above. (b) You may have seen that the voltage from a standard wall outlet is 120 volts. Verify that this is the root mean square value for V(t) given above. (Hìnt: Use the trigo- nometric identity sin? x = (1 – cos 2x)/2. This identity can be derived by letting y = x in the basic identity for cos(x + y), and then eliminating cos? x by using the iden- tity cos x = 1 - sin x.)
Chapter9: Current And Resistance
Section: Chapter Questions
Problem 84CP: In this chapter, most examples and problems involved direct current (DC). DC circuits have the...
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Transcribed Image Text:Voltage The electrical voltage from a standard wall outlet is
given as a function of time t by
V(t) = 170 sin(120 mt).
This is an example of alternating current, which is electric-
ity that reverses direction at regular intervals. The common
method for measuring the level of voltage from an alternating
current is the root mean square, which is given by
Root mean square =
P (1);^"S|
T
where T is one period of the current.
(a) Verify that T = 1/60 second for V(t) given above.
(b) You may have seen that the voltage from a standard
wall outlet is 120 volts. Verify that this is the root mean
square value for V(t) given above. (Hìnt: Use the trigo-
nometric identity sin? x = (1 – cos 2x)/2. This identity
can be derived by letting y = x in the basic identity for
cos(x + y), and then eliminating cos? x by using the iden-
tity cos x = 1 - sin x.)
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