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The RC size 12{ ital "RC"} {} time constant in heart defibrillation is crucial to limiting the time the current flows. If the capacitance in the defibrillation unit is fixed, how would you manipulate resistance in the circuit to adjust the RC size 12{ ital "RC"} {} constant τ size 12{τ} {} ? Would an adjustment of the applied voltage also be needed to ensure that the current delivered has an appropriate value?

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When making an ECG measurement, it is important to measure voltage variations over small time intervals. The time is limited by the RC size 12{ ital "RC"} {} constant of the circuit—it is not possible to measure time variations shorter than RC size 12{ ital "RC"} {} . How would you manipulate R size 12{R} {} and C size 12{C} {} in the circuit to allow the necessary measurements?

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Draw two graphs of charge versus time on a capacitor. Draw one for charging an initially uncharged capacitor in series with a resistor, as in the circuit in [link] , starting from t = 0 size 12{t=0} {} . Draw the other for discharging a capacitor through a resistor, as in the circuit in [link] , starting at t = 0 size 12{t=0} {} , with an initial charge Q 0 size 12{Q rSub { size 8{0} } } {} . Show at least two intervals of τ size 12{τ} {} .

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When charging a capacitor, as discussed in conjunction with [link] , how long does it take for the voltage on the capacitor to reach emf? Is this a problem?

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When discharging a capacitor, as discussed in conjunction with [link] , how long does it take for the voltage on the capacitor to reach zero? Is this a problem?

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Referring to [link] , draw a graph of potential difference across the resistor versus time, showing at least two intervals of τ size 12{τ} {} . Also draw a graph of current versus time for this situation.

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A long, inexpensive extension cord is connected from inside the house to a refrigerator outside. The refrigerator doesn’t run as it should. What might be the problem?

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In [link] , does the graph indicate the time constant is shorter for discharging than for charging? Would you expect ionized gas to have low resistance? How would you adjust R size 12{R} {} to get a longer time between flashes? Would adjusting R size 12{R} {} affect the discharge time?

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An electronic apparatus may have large capacitors at high voltage in the power supply section, presenting a shock hazard even when the apparatus is switched off. A “bleeder resistor” is therefore placed across such a capacitor, as shown schematically in [link] , to bleed the charge from it after the apparatus is off. Why must the bleeder resistance be much greater than the effective resistance of the rest of the circuit? How does this affect the time constant for discharging the capacitor?

An electrical circuit with a capacitor has an extra resistor R sub b l, called a bleeder, installed in parallel with the capacitor.
A bleeder resistor R bl size 12{R rSub { size 8{"bl"} } } {} discharges the capacitor in this electronic device once it is switched off.
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Problem exercises

The timing device in an automobile’s intermittent wiper system is based on an RC size 12{ ital "RC"} {} time constant and utilizes a 0 . 500-μF size 12{0 "." "500-"μF} {} capacitor and a variable resistor. Over what range must R size 12{R} {} be made to vary to achieve time constants from 2.00 to 15.0 s?

range 4 . 00 to 30 . 0 M Ω size 12{"range 4" "." "00 to 30" "." "0 M" %OMEGA } {}

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A heart pacemaker fires 72 times a minute, each time a 25.0-nF capacitor is charged (by a battery in series with a resistor) to 0.632 of its full voltage. What is the value of the resistance?

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The duration of a photographic flash is related to an RC size 12{ ital "RC"} {} time constant, which is 0 . 100 μs size 12{0 "." "100" μs} {} for a certain camera. (a) If the resistance of the flash lamp is 0 . 0400 Ω size 12{0 "." "0400" %OMEGA } {} during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is 800 size 12{"800"" k" %OMEGA } {} ?

(a) 2 . 50 μF size 12{2 "." "50 "mF} {}

(b) 2.00 s

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Practice Key Terms 3

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Source:  OpenStax, College physics for ap® courses. OpenStax CNX. Nov 04, 2016 Download for free at https://legacy.cnx.org/content/col11844/1.14
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