~christina~

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**1. Homework Statement**

A photographer's electronic flash unit consists of a 150.0-kΩ resistor in series with a 22-µF capacitor and a 12.0 V source of emf. The flashbulb is placed in parallel with the capacitor so that when a sufficient charge is stored on the capacitor switch S2 can be closed and the capacitor quickly discharges through the small resistance of the bulb, causing the flash. Suppose switch S2 remains open and at t = 0 s switch Sl is closed.

(a) At what time after the capacitor begins to charge has the current decreased to one-half its initial value?

(b) What is the charge on the capacitor at this time?

(c) What is the voltage across the capacitor at this time?

(d) Sketch graphs of the current through this circuit and the charge on the capacitor as functions of time (two graphs

http://img366.imageshack.us/img366/695/picture6ni5.th.jpg [Broken]

**2. Homework Equations**

[tex]\tau= RC [/tex]

[tex]I_i= \frac{\epsilon} {R} [/tex]

[tex]I(t)= \frac{\epsilon} {R} e^{\frac {-t} {RC}} [/tex]

**3. The Attempt at a Solution**

**a) At what time after the capacitor begins to charge has the current decreased to one-half its initial value?**

[tex]\tau= RC= (22x10^{-6} F)(1.50x10^5 \omega )= 3.3s [/tex]

__max current__: [tex]I_i= \frac{\epsilon} {R} = 12.0V/ 1.50x10^5 \omega= 8x10^{-5} A[/tex]

__current as a function of time__: [tex]I(t)= \frac{\epsilon} {R} e^{\frac {-t} {RC}} [/tex]

__half of the total current__: [tex]4x10^{-5}A [/tex]

**I think I would find the time this way but I'm not sure if it is right.**

__time it takes for the current to half__

[tex]I(t)= (8x10^-5A)\frac e^{\frac {-t} {3.3s}} [/tex]

[tex]0.5A= \frac e^{\frac {-t} {3.3s}} [/tex]

[tex]ln 0.5A= \frac{-t} {3.3s}} [/tex]

[tex]t= 2.287s[/tex]

**(b) What is the charge on the capacitor at this time?**

[tex]q(t)= C \epsilon (1-e^{-\frac{t} {RC}}) [/tex]

[tex]C \epsilon = (22x10^{-6}F)(12.0V)= 2.64x10^{-4}C[/tex]

[tex]q(t)= (2.64x10^{-4}C)(1-e^{-\frac{2.287s} {3.3s}}) [/tex]

[tex]q(t)= (2.64 x10^ {-4}C)(0.499941)=1.319844x10^{-4}C [/tex]

**(c) What is the voltage across the capacitor at this time?**

Not sure how to find this..

**(d) Sketch graphs of the current through this circuit and the charge on the capacitor as functions of time (two graphs**

wouldn't this look the typical graph of

charge vs time (exponential curve going up)=> |/|

current vs time (exponential curve going down)=> |\|

I'd appreciate it if someone could help me out with part c and also checking whether I did the other parts correctly.

Thanks alot

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