TYPICAL VOLTAGE, ENERGY, AND DISCHARGE TIME FOR A DEFIBRILLATOR GOAL Apply energy and power concepts to a capacitor. PROBLE M A fully charged defibrillator contains 1.20 kJ of energy stored in a 1.10×10^-4 F capacitor. In a discharge through a patient, 6.00×10² J of electrical energy is delivered

Question

TYPICAL VOLTAGE, ENERGY, AND DISCHARGE TIME FOR A DEFIBRILLATOR

GOAL Apply energy and power concepts to a capacitor.

PROBLE M A fully charged defibrillator contains [latex]1.20 \mathrm{~kJ}[/latex] of energy stored in a [latex]1.10 imes 10^{-4} \mathrm{~F}[/latex] capacitor. In a discharge through a patient, [latex]6.00 imes 10^{2} \mathrm{~J}[/latex] of electrical energy is delivered in [latex]2.50 \mathrm{~ms}[/latex]. (a) Find the voltage needed to store [latex]1.20 \mathrm{~kJ}[/latex] in the unit. (b) What average power is delivered to the patient?

STRATEGY Because we know the energy stored and the capacitance, we can use Equation [latex]16.17[/latex]

[latex]P E_{C} =\frac{1}{2} Q \Delta V =\frac{1}{2} C(\Delta V)^2 = \frac{Q^2}{2C}[/latex] [16.17]

to find the required voltage in part (a). For part (b), dividing the energy delivered by the time gives the average power.

Accepted Answer

(a) Find the voltage needed to store [latex]1.20 \mathrm{~kJ}[/latex] in the unit.

Solve Equation 16.17 for [latex]ΔV[/latex]:

[latex]\begin{aligned}P E_{C} &=\frac{1}{2} C \Delta V^{2} \\Delta V &=\sqrt{\frac{2 imes P E_{C}}{C}} \&=\sqrt{\frac{2\left(1.20 imes 10^{3} \mathrm{~J} ight)}{1.10 imes 10{ }^{-4} \mathrm{~F}}} \&=4.67 imes 10^{3} \mathrm{~V}\end{aligned}[/latex]

(b) What average power is delivered to the patient?

Divide the energy delivered by the time:

[latex]\begin{aligned}P_{\mathrm{av}} &=\frac{ ext { energy delivered }}{\Delta t}=\frac{6.00 imes 10^{2} \mathrm{~J}}{2.50 imes 10^{-3} \mathrm{~s}} \&=2.40 imes 10^{5} \mathrm{~W}\end{aligned}[/latex]

REMARKS The power delivered by a draining capacitor isn't constant, as we'll find in the study of [latex]R C[latex] circuits in Topic 18 . For that reason, we were able to find only an average power. Capacitors are necessary in defibrillators because they can deliver energy far more quickly than batteries. Batteries provide current through relatively slow chemical reactions, whereas capacitors can quickly release charge that has already been produced and stored.

Question 16.10: TYPICAL VOLTAGE, ENERGY, AND DISCHARGE TIME FOR A DEFIBRILLA...

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