A heart defibrillator being used on a patient has an R C...

A heart defibrillator being used on a patient has an $R C$ 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 - $\mu$ 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 $12.0 \mathrm{kV}$, how long does it take to decline to $6.00 \times 10^{2} \mathrm{V} ?$

Key Concepts

RC Time Constant

The RC time constant, denoted by the product of resistance (R) and capacitance (C), characterizes the rate at which a capacitor charges or discharges in an RC circuit. It is a measure of the time required for the voltage across the capacitor to either rise to approximately 63% of its final value during charging or fall to about 37% of its initial value during discharging. This concept is crucial in analyzing the transient response of circuits, including those found in medical devices like defibrillators.

Capacitance

Capacitance is the measure of a capacitor's ability to store electrical charge per unit voltage. It is expressed in farads (F), and in practical applications, smaller units such as microfarads (?F) are commonly used. Understanding capacitance is essential for determining how energy is stored and subsequently released in a circuit, impacting the circuit's timing and performance characteristics.

Resistance

Resistance is the property of a material or component that impedes the flow of electrical current, measured in ohms (?). In an RC circuit, resistance plays a key role in regulating the speed at which a capacitor charges or discharges. The value of resistance can be derived from the known RC time constant and the capacitance, providing insight into the overall behavior of the circuit during transient events.

Exponential Decay in RC Circuits

Exponential decay in RC circuits describes how the voltage across a capacitor decreases over time when the capacitor discharges through a resistor. This behavior is modeled by the equation V(t) = V?e^(–t/RC), where V? is the initial voltage. The concept is vital for understanding the timing of voltage drops in various applications, including the precise delivery of energy in medical devices, as it helps determine how long it takes for the voltage to reach a specified level.

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