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# For full credit, show your calculations, beginning with a formula and including units in all calculations and answers. (10 points) Camera Electronic Flash–An electronic flashgun has a 1000-μF capacitor that is charged to 100 V. (Remember that 1000 μF = 1000 x 10−6 F. How much energy is stored by the capacitor? What is the charge on the capacitor? When the photographer takes a picture, the flash fires for 1/2000 s. What is the average current through the flash tube? Find the power delivered to the flashtube. After a picture is taken, the capacitor has to be recharged by a power supply that delivers a maximum current of 10 mA. How long will it take to charge the capacitor?   (3 points) Computer Keyboard – In one kind of computer keyboard, each key is attached to one plate of a parallel-plate capacitor; the other plate is fixed in position, as in the figure below. The capacitor is maintained at a constant potential difference of 5.0 V by an external circuit. When the key is pressed down, the top plate moves closer to the bottom plate, changing the capacitance and causing charge to flow through the circuit. If each plate is a square of side 6.0 mm and the plate separation changes from 4.0 mm to 1.2 mm when a key is pressed, how much charge flows through the circuit?(Hint: since the potential difference ΔV is kept constant, the charge that flows through the circuit is ΔQ = Qf – Qi) Assume that there is air between the plates instead of a flexible insulator.   (8 points) Automated External Defibrillator (AED) – The immediate cause of many deaths is ventricular defibrillation, an uncoordinated quivering of the heart, as opposed to proper beating. An electric shock to the chest can cause momentary paralysis of the heart muscle, after which the heart will sometimes start coordinated beating again. A defibrillator is a device that applies a strong electric shock to the chest over a time of a few milliseconds. The device contains a capacitor of a few microfarads, charged to several thousand volts. Electrodes called paddles, about 8 cm across and coated with conducting paste, are held against the chest on both sides of the heart. Their handles are insulated to prevent injury to operator, who calls, “Clear!” and pushes a button on one paddle to discharge the capacitor through the patient’s chest. (Source:Serway, R.A. and Vuille, C., 2007, Essentials of College Physics, Brooks/Cole, Belmont CA, p. 444, Chap. 16.) A defibrillator passes a brief burst of current through the heart to restore normal beating. In one such defibrillator, a 50.0-μF capacitor is charged to 6.0 kV. Paddles are used to make an electric connection to the patient’s chest. A pulse of current lasting 1.2 mspartially discharges the capacitor through the patient. The electrical resistance of the patient (from paddle to paddle) is 240 Ω. What is the initial energy stored in the capacitor? How much charge is on each plate of the fully charged capacitor? How much energy is dissipated in the patient during the 1.2 ms? (Hint: Use the known values of R and C to calculate the time constant τ.) What average power is delivered to the patient during the 1.2 ms?   The cutoff frequency is defined for an R-C circuit as: f_c= 1/2πRC And for an R-Lcircuit, f_c= R/2πL (8 points) Low Pass Filter – In this problem you will design two low pass filters. For one use R-C, for the other use R-L . Design them to have the same cutoff frequency of 1000 Hz and using a 1-kΩ resistor in each case. In the R-C circuit, what value must the capacitor have? Draw a picture of the R-C low pass filter. In the R-L circuit, what value must the inductor have? Draw a picture of the R-L low pass filter.   (8 points) High Pass Filter – In this problem you will design two high pass filters. For one use R-C, for the other use R-L . Design them to have the same cutoff frequency of 500 Hz and using a 1-kΩresistor in each case. In the R-C circuit, what value must the capacitor have? Draw a picture of the R-C high pass filter. In the R-L circuit, what value must the inductor have? Draw a picture of the R-L high pass filter. (3 points)Intermittent Windshield Wipers – A charging RC circuit controls the intermittent windshield wipers in a car. The applied voltage is 12.0 V. The wipers are triggered when the voltage across the 125-μF capacitor reaches 10.0 V; then the capacitor is quickly discharged (through a much smaller resistor) and the cycle repeats. What resistance should be used in the charging circuit if the wipers are to operate once every 1.80 s? Remember that 125 μF = 125 x 10−6 F. Hint: Solve for R usingV_C=E(1-e^(-t/τ))

For full credit, show your calculations, beginning with a formula and including units in all calculations and answers.

1. (10 points) Camera Electronic Flash–An electronic flashgun has a 1000-μF capacitor that is charged to 100 V. (Remember that 1000 μF = 1000 x 10−6
• How much energy is stored by the capacitor?

• What is the charge on the capacitor?

• When the photographer takes a picture, the flash fires for 1/2000 s. What is the average current through the flash tube?

• Find the power delivered to the flashtube.

• After a picture is taken, the capacitor has to be recharged by a power supply that delivers a maximum current of 10 mA. How long will it take to charge the capacitor?

1. (3 points) Computer Keyboard – In one kind of computer keyboard, each key is attached to one plate of a parallel-plate capacitor; the other plate is fixed in position, as in the figure below. The capacitor is maintained at a constant potential difference of 5.0 V by an external circuit. When the key is pressed down, the top plate moves closer to the bottom plate, changing the capacitance and causing charge to flow through the circuit. If each plate is a square of side 6.0 mm and the plate separation changes from 4.0 mm to 1.2 mm when a key is pressed, how much charge flows through the circuit?(Hint: since the potential difference ΔV is kept constant, the charge that flows through the circuit is ΔQ = Qf – Qi) Assume that there is air between the plates instead of a flexible insulator.

1. (8 points) Automated External Defibrillator (AED)

The immediate cause of many deaths is ventricular defibrillation, an uncoordinated quivering of the heart, as opposed to proper beating. An electric shock to the chest can cause momentary paralysis of the heart muscle, after which the heart will sometimes start coordinated beating again. A defibrillator is a device that applies a strong electric shock to the chest over a time of a few milliseconds. The device contains a capacitor of a few microfarads, charged to several thousand volts. Electrodes called paddles, about 8 cm across and coated with conducting paste, are held against the chest on both sides of the heart. Their handles are insulated to prevent injury to operator, who calls, “Clear!” and pushes a button on one paddle to discharge the capacitor through the patient’s chest. (Source:Serway, R.A. and Vuille, C., 2007, Essentials of College Physics, Brooks/Cole, Belmont CA, p. 444, Chap. 16.)

A defibrillator passes a brief burst of current through the heart to restore normal beating. In one such defibrillator, a 50.0-μF capacitor is charged to 6.0 kV. Paddles are used to make an electric connection to the patient’s chest. A pulse of current lasting 1.2 mspartially discharges the capacitor through the patient. The electrical resistance of the patient (from paddle to paddle) is 240 Ω.

• What is the initial energy stored in the capacitor?

• How much charge is on each plate of the fully charged capacitor?

• How much energy is dissipated in the patient during the 1.2 ms? (Hint: Use the known values of R and C to calculate the time constant τ.)

• What average power is delivered to the patient during the 1.2 ms?

The cutoff frequency is defined for an R-C circuit as:

And for an R-Lcircuit,

1. (8 points) Low Pass Filter – In this problem you will design two low pass filters. For one use R-C, for the other use R-L .  Design them to have the same cutoff frequency of 1000 Hz and using a 1-kΩ resistor in each case.
• In the R-C circuit, what value must the capacitor have?

• Draw a picture of the R-C low pass filter.

• In the R-L circuit, what value must the inductor have?

• Draw a picture of the R-L low pass filter.

1. (8 points) High Pass Filter – In this problem you will design two high pass filters. For one use R-C, for the other use R-L .  Design them to have the same cutoff frequency of 500 Hz and using a 1-kΩresistor in each case.
• In the R-C circuit, what value must the capacitor have?

• Draw a picture of the R-C high pass filter.

• In the R-L circuit, what value must the inductor have?

• Draw a picture of the R-L high pass filter.

1. (3 points)Intermittent Windshield Wipers – A charging RC circuit controls the intermittent windshield wipers in a car. The applied voltage is 12.0 V. The wipers are triggered when the voltage across the 125-μF capacitor reaches 10.0 V; then the capacitor is quickly discharged (through a much smaller resistor) and the cycle repeats. What resistance should be used in the charging circuit if the wipers are to operate once every 1.80 s? Remember that  125 μF = 125 x 10−6 Hint:  Solve for R using

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