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Lecture 21: Rms Vs. Peak, Self

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Phy2005 Applied Physics II Spring 2016 Announcements: • • • • Test 2 Wednesday, March 23 2 practice tests posted on course Tests page Review session in class March 21 in class + 1 evening tba PH travel next week APS Spring meeting; Prof. Lee subs Science news page “Total Solar Eclipse Will End the Day Before It Begins” Link to NYT video Last time: Eddy currents induced current in metal: Eddy current I Non-magnetic metal plate There is an emf around any loop where flux is changing! Last Time xrms  x x = Asin(2ft) 2 x  xo sin( 2ft) AV x x0 xrms 0 T -A xrms xo   0.707 xo 2 T (period) “repeat time” frequency: f = 1/T angular frequency: w = 2f = 2/T t Last time: Iron Core Vp/Vs = Np/Ns V AC Np Ns p=primary s=secondary Neutral Hot GND http://www.howstuffworks.com/ Power Transmission Gainesville has a population of 120,000. On average approximately 200 W/person of electric power is required. Let’s assume that GRU transmits power with 120 V. How much current should be carried in the power line? Pt = 120,000 x 200 W = 24,000,000 W = 24 MW P = IV, I = P/V = 24,000,000/120 = 200,000 A However, if we deliver power with 500,000 V, I = 24,000,000/500,000 = 48 A Now Joule heating (I2R) due to wire resistance (R) is reduced By (48/200,000)2 = 5.8 x 10-8 From now on, when you see voltage or current in lower case, those indicate AC voltage or current. I: DC current i: AC current V: DC voltage v: AC voltage R R P = V2/R = I2R = IV V, V2 V = Vo v = vosin(2ft) T = 1/f t P = Vo2/R: constant in time P = (vosin(2t))2/R: varying in time v2 P = (vosin(2t))2/R: varying in time t We need to take the average (mean) of the time dependent power over one cycle!!

= <(vosin(2ft))2>/R <(vosin(2ft))2> = vo2/2 So on average replace vo sin( 2ft)  vo  0.707vo 2 Root Mean Square (rms) Root does not mean square! You have a variable x. Square, take average, and put square-root. xrms  xrms  x  xo sin( 2ft) x x2 2 AV AV xrms xo   0.707 xo 2 Use rms values of v and i for AC to evaluate average power.

= vrms2/R = irms2R = irmsvrms Ex 22-2 A sinusoidal AC voltage source with a 20 V amplitude and a 15 Hz frequency is applied across an electric heater with 10 W resistance. (a) Write down a mathematical expression for the voltage. (b) What is the rms value of the voltage source? (c) How much power is dissipated in this heater? (a) v = 20sin(94.2t) (b) vrms = 14.14 V (c)

= 20 W Ex 22-3 A 75-W light bulb is operated on its rated 120 V/60 Hz power. Find the rms current drawn by the bulb.

= irmsvrms irms = 75/120 = 0.625 A ACADEMIC HONESTY Each student is expected to hold himself/herself to a high standard of academic honesty. Under the UF academic honesty policy. Violations of this policy will be dealt with severely. There will be no warnings or exceptions. Q1 A current is given by i = 2sin(40t) A. Find the peak current (A), the rms current (B), and the frequency. 1. 2. 3. 4. (A) 2A 4A 2 A 4 A (B) 2.83 A 2.83 A 1.41 A 1.41 A (C) 40 Hz 20 Hz 6.37 Hz 12.7 Hz R C L http://www.educatorscorner.com/ Loop area: A Length of coil: ℓ Winding density: n = N/ ℓ Increase current through the coil from 0 to di in dt. For a long solenoid B = monI n: number of turns/m Causes flux change for each loop from F = 0 to F = AB where B = mondi Vind = - n ℓ dF/dt = - n ℓ A(mon)di/dt = - n2moA ℓ (di/dt) L: self inductance geometrical quantity Vind = -L(di/dt) [L] = Henry Joseph Henry 1797-1878 American physicist Henry discovered the electromagnetic phenomenon of self-inductance. He also discovered mutual inductance independently of Michael Faraday, (1791–1867), though Faraday was the first to make the discovery and publish his results.[2][3][4] Henry developed the electromagnet into a practical device. He invented a precursor to the electric doorbell (specifically a bell that could be rung at a distance via an electric wire, 1831)[5] and electric relay (1835).[6] The SI unit of inductance, the henry, is named in his honor.