Physics
Physics
3rd Edition
ISBN: 9781259233616
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 18, Problem 92P

(a)

To determine

Find the initial energy stored in the capacitor.

(a)

Expert Solution
Check Mark

Answer to Problem 92P

The initial energy stored in the capacitor is 900 J.

Explanation of Solution

Write the equation for energy.

U0=12CV02 (I)

Here, U0 is the initial energy, C is the capacitance and V0 is the initial voltage.

Conclusion:

Substitute 6.0×103 V for V0 and 50.0×106 F for C in equation I.

U0=12(50.0×106 F)(6.0×103 V)2=900 J

Therefore, the initial energy stored in the capacitor is 900 J.

(b)

To determine

Find the initial current through the patient.

(b)

Expert Solution
Check Mark

Answer to Problem 92P

The initial current through the patient is 25 A.

Explanation of Solution

Write the equation for current,

I0=V0R (II)

Here, R is the resistance, V0 is the initial voltage and I0 is the initial current

Conclusion:

Substitute 6.0×103 V for V0 and 240 Ω for R in equation II.

I0=6.0×103 V240 Ω=25 A

Therefore, the initial current through the patient is 25 A.

(c)

To determine

Find the energy dissipated in the patient during 1.0 ms of time.

(c)

Expert Solution
Check Mark

Answer to Problem 92P

The energy dissipated in the patient during 1.0 ms of time is 140 J.

Explanation of Solution

Write the equation for voltage with respect to time,

VC=V0et/τ (III)

Here, VC  is the voltage across the capacitor, V0 is the initial voltage, t is the time and τ is the time constant.

Write the equation for energy.

U=12CVC2 (IV)

Here, U is the energy, C is the capacitance and VC is the voltage across the capacitor.

Then, the energy dissipated in the patient is,

U0U

Substitute equation III in IV and then in the above equation.

U0U=U012C(V0et/τ)2=U0(1e2t/RC) (V)

Conclusion:

Substitute 900 J for U0 , 0.0010 s for t , 240 Ω for R and 50.0×106 F for C in equation V.

U0U=(900 J)(1e2(0.0010 s)/(240 Ω)(50.0×106 F))=140 J

Therefore, the energy dissipated in the patient during 1.0 ms of time is 140 J.

(d)

To determine

Compare the average power supplied by the power source with the power delivered by the patient.

(d)

Expert Solution
Check Mark

Answer to Problem 92P

The average power supplied by power source is 0.0033 times that delivered to the patient.

Explanation of Solution

Write the average power by source and patient the divide them.

PsourcePpatient=U0ΔtsourceUΔtpatient=U0ΔtpatientUΔtsource (VI)

Conclusion:

Substitute 900 J for U0 , 138 J for U, 1.0×103 s for Δtpatient and 2.0 s for Δtsource in equation VI.

PsourcePpatient=(900 J)(1.0×103 s)(138 J)(2.0 s)=0.0033

Therefore, the average power supplied by power source is 0.0033 times that delivered to the patient.

(e)

To determine

Why the capacitors are used in the defibrillator.

(e)

Expert Solution
Check Mark

Answer to Problem 92P

The capacitors can produce much higher burst of current to the patient than the power source.

Explanation of Solution

The capacitor used in the defibrillator can produces much higher burst of current to the patient when compared to the burst produces by the power source.

Conclusion:

Therefore, the capacitors are used to produce burst in current to the patients.

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Chapter 18 Solutions

Physics

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