In a defibrillator (see Example 17.12 ), a charged capacitor...

In a defibrillator (see Example 17.12 ), a charged capacitor is connected to paddles that make electrical contact with the patient's skin. If gel is applied to the patient's chest to make a good connection between the paddles and the skin, the effective resistance through which the capacitor discharges is 52.0 \Omega. (a) To what voltage must the capacitor be charged to generate a maximum current of $40.0 \mathrm{A} ?$ (b) If the current $1.00 \mathrm{ms}$ later is $10.0 \mathrm{A},$ what is the capacitance? (c) Why does a paramedic shout "Clear!" before administering the shock?

In a defibrillator (see Example 17.12 ), a charged capacitor is connected to paddles that make electrical contact with the patient's skin. If gel is applied to the patient's chest to make a good connection between the paddles and the skin, the effective resistance through which the capacitor discharges is 52.0 \Omega. (a) To what voltage must the capacitor be charged to generate a maximum current of $40.0 \mathrm{A} ?$
(b) If the current $1.00 \mathrm{ms}$ later is $10.0 \mathrm{A},$ what is the capacitance?
(c) Why does a paramedic shout "Clear!" before administering the shock?

Key Concepts

Capacitor Energy Storage

A capacitor is a device that stores electrical energy in an electric field. In circuits, capacitors are used to store charge and release it as needed, such as delivering a rapid burst of current. This principle is central to understanding how defibrillators use a precharged capacitor to deliver a controlled shock to a patient.

RC Circuit

An RC circuit consists of a resistor and a capacitor connected in series or parallel. When a charged capacitor discharges through a resistor, the current and voltage in the circuit do not drop instantaneously but rather decay exponentially over time. This behavior is crucial for analyzing the transient response of the circuit during a discharge.

Exponential Decay in RC Circuits

The current in an RC discharging circuit follows the relationship I(t) = (V?/R) e^(?t/RC), where V? is the initial voltage, R is the resistance, C is the capacitance, and t is time. This exponential decay characterizes how quickly the current diminishes as the capacitor releases its stored energy, and it is essential for determining parameters such as maximum initial current and later current values.

Time Constant

The time constant in an RC circuit, given by ? = RC, determines the rate at which the current and voltage decay. A larger time constant means the system discharges more slowly, while a smaller time constant means a faster discharge. This concept is important when analyzing transient phenomena in circuits, including calculating required capacitance or predicting current at a specific time.

Electrical Safety Protocols

Electrical safety protocols encompass the practices and precautions taken to protect both patients and operators when dealing with electrical devices. In medical contexts like defibrillators, clear communication—such as shouting 'Clear!'—ensures that all personnel are aware that a high-energy discharge is imminent, thereby preventing accidental injury and ensuring the safe administration of the shock.

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