A heart defibrillator being used on a patient has an RC time...

A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an $8.00-\mu \mathrm{F}$ capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to $6.00 \times 10^{2} \mathrm{v} ?$

A heart defibrillator being used on a patient has an RC time constant of 10.0 ms due to the resistance of the patient and the capacitance of the defibrillator. (a) If the defibrillator has an $8.00-\mu \mathrm{F}$ capacitance, what is the resistance of the path through the patient? (You may neglect the capacitance
of the patient and the resistance of the defibrillator.) (b) If the initial voltage is 12.0 kV, how long does it take to decline to $6.00 \times 10^{2} \mathrm{v} ?$

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Key Concepts

RC Time Constant

The RC time constant (? = RC) is a measure of the time it takes for a capacitor to charge or discharge through a resistor. It characterizes the exponential rate at which the voltage across a capacitor falls (or rises) towards its asymptotic value and is a fundamental concept in the analysis of RC circuits.

Capacitor Discharge and Exponential Decay

In an RC circuit, the voltage across a discharging capacitor decreases exponentially over time according to the relationship V(t) = V? exp(-t/RC). This principle is used to determine the time it takes for the voltage to reach a specified fraction of its initial value using logarithmic manipulation of the exponential decay formula.

Resistance Determination in RC Circuits

When the RC time constant and the capacitance are known, the resistance can be calculated directly from the product ? = RC. This concept is crucial in medical devices and other applications where accurate timing of the voltage decay is required.

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