PHY2049ch27C-28A%282-19-10%29

PHY2049ch27C-28A%282-19-10%29 - RC Circuit Examples In an...

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RC Circuit Examples t q(t) C [1 e ] τ =ξ− For a charging capacitor, The full charge is, f qC = ξ We are asked for the time when, f q 0.99q 0.99C = In an RC circuit what multiple of the time constant gives the time taken for an initially uncharged capacitor to be charged to 99% of its full charge ? RC τ = t 0.99C C [1 e ] τ = ξ (t in q(t)) →∞ ξ So solve, for t .
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t 0.99 1 e τ = t e 1 0.99 τ = t ln e ln(0.01) τ ⎛⎞ = ⎜⎟ ⎝⎠ t ln(0.01) 4.61 −= = τ t 4.61 = τ
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Example 2 20 V 2.5 μ F The switch is closed for at least 10RC in charging the capacitor. From when the switch is then opened how long does it take for the potential difference across the capacitor to become 2 V. A discharging capacitor obeys o t RC qq e = q qC V V C =→ = Now, So, o t RC q q Ve CC == We solve this for the time when V = 2 V .
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With the switch initially closed for 10RC the capacitor becomes fully charged. Since for charging, o t RC q Ve C = o t RC VC e q = o t RC VC ln ln e q ⎛⎞ = ⎜⎟ ⎝⎠ o VC t ln qR C =− o VC tR C l n q We need the charge, q o , on the capacitor when the switch is opened and the resistance , R, through which it discharges. 20 V 2.5 μ F t RC t qC [ 1 e ] C >>τ = ξ− ξ o = ξ For the resistance we have R( 6 6 ) | | 6 + Ω Ω
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20 V 2.5 μ F R1 2| | 6 =ΩΩ 12 6 R4 12 6 Ω⋅ Ω == Ω Ω+ Ω Then with o VC VC t RCln qC ⎛⎞ =− ⎜⎟ ξ ⎝⎠ o V2 V tR C l n ( 4 ) ( 2 . 5 F ) l n 20V =− Ω μ ξ t2 3 s = μ
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HITT–2/19/10 CLOSED BOOK In the circuit to the right the colored circles are meters: 1) 1 measures the current going through R 1 and R 2 and 2 measures the current through R 1 only. 1 2 2) 1 measures the current going through R 1 and R 2 and 2 measures the voltage across R1 only. 3) 1 measures the current going through R 1 only and 2 measures the voltage across R 1 only. 4) 1 measures the voltage going through R 1 and R 2 and 2 measures the current through R 1 only.
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Magnetic Fields You may have seen this method of visualizing the magnetic field lines surrounding a bar magnet . Here a bar magnet lies below a stiff piece of paper and iron filings (thin slivers of iron) are sprinkled onto the paper. The iron slivers that fall nearest the magnet’s ends are attracted to them. Those that are further away aren’t pulled hard enough to overcome the friction with the paper but they re–orient themselves to line up along the magnetic field lines letting us “see” the magnetic field.
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Simple experiments with two bar magnets show that they can interact with an attraction if oriented one way or a repulsion if one of them is flipped around. Labeling the two poles of a magnet north and south we find that N–N and S–S repel while N–S attract.
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Iron filings can help us visualize the magnetic fields here as well.
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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PHY2049ch27C-28A%282-19-10%29 - RC Circuit Examples In an...

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