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UT Arlington PHYS 1444 - RC circuit

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Wednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu1PHYS 1444 – Section 003Lecture #14Wednesday, Oct. 19, 2005Dr. Jaehoon Yu• RC circuit example• Discharging RC circuits• Application of RC circuits• Magnets• Magnetic field• Earth’s magnetic field• Magnetic field by electric current• Magnetic force on electric currentWednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu2Announcements• There is a colloquium at 4pm in SH103– All Physics faculty will introduce their own research– An extra credit opportunity • Extra credit opportunity was announced on Sept. 14th:– 15 point extra credit for presenting a professionally prepared 3 page presentation on any one of the exhibits at the UC gallery (till 9/16) and the subsequent themed displays at the central library.• Must include what it does, how it works and where it is used. Possibly how it can be made to perform better.• Due: Oct. 19, 2005Wednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu3• Since and• What can we see from the above equations?– Q and VCincrease from 0 at t=0 to maximum value Qmax=C and VC= .• In how much time?– The quantity RC is called the time constant, τ, of the circuit• τ=RC, What is the unit?– What is the physical meaning?• The time required for the capacitor to reach (1-e-1)=0.63 or 63% of the full charge• The current is Analysis of RC Circuits()1tRCQC eε−=−()1tRCCVeε−=−Sec.tRCdQIedt Rε−==Wednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu4Example 26 – 12 RC circuit, with emf. The capacitance in the circuit of the figure is C=0.30µF, the total resistance is 20kΩ, and the battery emf is 12V. Determine (a) the time constant, (b) the maximum charge the capacitor could acquire, (c) the time it takes for the charge to reach 99% of this value, (d) the current I when the charge Q is half its maximum value, (e) the maximum current, and (f) the charge Q when, the current I is 0.20 its maximum value. (a) Since τ=τ=We obtain maxQ=(c) Since The current when Q is 0.5Qmax(b) Maximum charge is Q =For 99% we obtain 0.99Cε=0.01;tRCe−=2ln10;tRC−=−t=(d) Sinceε=I=We obtain I=(e) When is I maximum?I=when Q=0:(f) What is Q when I=120mA?Q=()64460.30 10 2 10 2.9 1012 1.2 10 C−− −=× ⋅×=×−×RC320 10×⋅60.30 10−×=36.0 10 sec−×Cε=60.30 10−⋅×12=63.6 10 C−×Cε()1tRCe−−()1tRCCeε−−2ln10RC⋅= 4.6RC=328 10 sec−×IRQC+()QCε−R()6631.8 10 0.30 10 20 1012−−×××=−4310A−×312 20 10×=4610A−×()CIRε=−Wednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu5– The rate at which the charge leaves the capacitor equals the negative the current flows through the resistor• I=-dQ/dt. Why negative?• Since the current is leaving the capacitor – Thus the voltage equation becomes a differential equationDischarging RC Circuits• When a capacitor is already charged, it is allowed to discharge through a resistance R.– When the switch S is closed, the voltage across the resistor at any instant equals that across the capacitor. Thus IR=Q/C.dQRdt−=dQQ=Rearrange termsQCdtRC−Wednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu6– Now, let’s integrate from t=0 when the charge is Q0to t when the charge is Q– The result is– Thus, we obtain– What does this tell you about the charge on the capacitor?• It decreases exponentially w/ time and w/ time constant RC• Just like the case of charging– The current is:• The current also decreases exponentially w/ time w/ constant RCDischarging RC Circuits00QtQdQdtQRC=−∫∫0lnQQQ=()0tRCQt Qe−=I=()0tRCIt Ie−=0lnQQ=tRC−dQdt−=0tRCQeRC−What is this?Wednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu7Example 26 – 13 Discharging RC circuit. In the RC circuit shown in the figure the battery has fully charged the capacitor, so Q0=Cε. Then at t=0, the switch is thrown from position a to b. The battery emf is 20.0V, and the capacitance C=1.02µF. The current I is observed to decrease to(a) Since the current reaches to 0.5 of its initial value in 40µs, we can obtain τ=(b) The value of Q at t=0 is0Q =0.50 of its initial value in 40µs. (a) what is the value of R? (b) What is the value of Q, the charge on the capacitor, at t=0? (c) What is Q at t=60µs? ()0tRCIt Ie−=000.5tRCIIe−=ln 0.5 ln 2tRC−==−R =For 0.5I0Rearrange termsSolve for RThe RC time(c) What do we need to know first for the value of Q at t=60µs?Thus()60Qt sµ==()ln 2tC=()6640 10 1.02 10 l n 2 56.6−−××⋅=ΩmaxQ=Cε=620.0 20.41.02 10Cµ−⋅=×RC=656.6 1.02 10 57.7 sµ−⋅×=0tRCQe−=6 60 57.720.4 10 7.2sseCµµµ−−×⋅ =Wednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu8• What do you think the charging and discharging characteristics of RC circuits can be used for?– To produce voltage pulses at a regular frequency–How?• The capacitor charges up to a particular voltage and discharges• A simple way of doing this is to use breakdown of voltage in a gas filled tube– The discharge occurs when the voltage breaks down at V0– After the completion of discharge, the tube no longer conducts– Then the voltage is at V0’ and it starts charging up– How do you think the voltage as a function of time look?» A sawtooth shape• Pace maker, intermittent windshield wiper, etcApplication of RC CircuitsWednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu9Magnetism• What are magnets?– Objects with two poles, north and south poles• The pole that points to geographical north is the north pole and the other is the south pole– Principle of compass– These are called magnets due to the name of the region, Magnesia, where rocks that attract each other were found• What happens when two magnets are brought to each other?– They exert force onto each other– What kind?– Both repulsive and attractive forces depending on the configurations• Like poles repel each other while the unlike poles attractWednesday, Oct. 19, 2005 PHYS 1444-003, Fall 2005Dr. Jaehoon Yu10Magnetism• So the magnet poles are the same as the electric charge?– No. Why not?– While the electric charges (positive and negative) can be isolated the magnet poles cannot be isolated.– So what happens when a magnet is cut?• If a magnet is cut, two magnets are made.• The more they get cut, the more magnets are made– Single pole magnets are called the monopole but


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