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 + March 21 6pm NPB 2205 PH travel next week APS Spring meeting; Prof. Lee subs

Science news page Link to NYT article American Meteor Society

Last time Use rms values of v and i for AC to evaluate average power. = v rms 2 /R = i rms 2 R = i rms v rms V ind = - n ℓ  /  t = - n ℓ A(  o n)  i/  t = - n 2  o A ℓ (  i / t) L: self inductance: V ind =-L  i / t geometrical quantity [L] = Henry

r = 1 cm ℓ = 2.5 cm n = 10 turns/cm = 0.01 m = m = 1000 turns/m L = n 2  o A ℓ = (1000) 2 (4  x )(  x )0.025 = 9.9 x H = 9.9  H Calculate L for a solenoid:

Ex 22-4 A steady current of 5.0 A is flowing through a coil with 2 H self inductance. The current is suddenly stopped in 0.01 s. How large an EMF would be induced in the coil? V ind = -L (  i/  t) = -(2)(-5/0.01) = 1000 V Connect and disconnect circuits with inductive elements especially carefully!!!!

Level Time

RC Circuit Q = C V V Constant I-source I Q V

V = 0 VcVc t = 0: V c = 0I 0 = (V – V c )/R = V/R t = t 1 : V c = V 1 (>0)I 1 = (V –V 1 )/R (< I 0 ) VcVc t t = t 2 : V c = V 2 (> V 1 >0) I 2 = (V – V 2 )/R (< I 1 < I 2 ) V

V VcVc t V c = V (1 – e -t/RC ) t c = RC V c = V (1 – e -1 ) = 0.63 V RC: time constant 0.63V e = When a capacitor with a capacitance C is connected to a constant voltage source V o through a series resistor R, (i) The potential difference across the capacitor increases not linearly but exponentially. (ii) The potential difference reaches 63% of the maximum value (0.63Vo) at time t c = RC.

t V = V o e -t/RC 0.37 RC R C +Q -Q V c = Q/C + When a capacitor (C ) initially charged with Q is discharged through a series resistor R, (i)The amount of charge on the capacitor (voltage) decreases exponentially. (ii) 63% of the total charge (0.63Q) will be discharged at time t c = RC.

Ex 23-1 A 100  F capacitor is fully charged with 5 V DC source. This capacitor is discharged through 10 K  resistor for 1 s. How much of charge is left in the capacitor in C? Total amount of charge: Q = C V = (100 x F)(5 V) = 5 x C Time constant: t = RC = (100 x F)(10 x 10 3 Ohm) = 1 s Since Q is proportional to V, after one time constant (100 – 63)% of initial charge is left: Q = 0.37 (5 x ) C

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Q1 (24.11) An uncharged 2-  F capacitor is connected in series with a switch, a 5x10 6  resistor, and a 12V battery. Find the current in the circuit just after switch is closed, and the time constant. (I) (  ) x A 10 s x 10 6 A 3.2 s x A 2.7 s A 1.41 s

Electromagnetic WAVES

y = sin(kx) Traveling sin(kx) with a velocity v: y = sin{k(x-vt)} x t Wavelength:  k period: T Frequency: f = 1/T v = f

Any traveling wave satisfies this equation. Sound Wave Sound is a longitudinal mechanical wave that travels through an elastic medium. The speed of sound in air at 27  C is 347 m/s. The middle A note (A4) has 440 Hz frequency. We can use the above equation to calculate the wavelength of the middle A note sound wave.  = v/f = (347/440) m

From quantities present in his equations Maxwell was able to calculate the speed with which electromagnetism moves Turned out to be c, the speed of light (known from Romer astronomical expts. in 17 th century.) “We can scarcely avoid the inference that light consists of the transverse undulations of the same medium which is the cause of magnetic and electric phenomena” -- Maxwell Light was known to be a wave (Young experiment 1801)

c= x 10 8 m/s Fiat Lux! Velocity of the wave solutions to Maxwell equations Note  0,  0 come from laboratory measurements of electricity and magnetism