For the values noted in the passage above, what is the time constant for the discharge of the capacitor?

A. \(3.2 \mu \mathrm{s}\)

B. \(160 \mu \mathrm{s}\)

C. \(3.2 \mathrm{~ms}\)

D. \(160 \mathrm{~ms}\)

A defibrillator is designed to pass a large current through a patient's torso in order to stop dangerous heart rhythms. Its key part is a capacitor that is charged to a high voltage. The patient's torso plays the role of a resistor in an \(R C\) circuit. When a switch is closed, the capacitor discharges through the patient's torso. A jolt from a defibrillator is intended to be intense and rapid; the maximum current is very large, so the capacitor discharges quickly. This rapid pulse depolarizes the heart, stopping all electrical activity. This allows the heart's internal nerve circuitry to reestablish a healthy rhythm.

A typical defibrillator has a \(32 \mu \mathrm{F}\) capacitor charged to \(5000 \mathrm{~V}\). The electrodes connected to the patient are coated with a conducting gel that reduces the resistance of the skin to where the effective resistance of the patient's torso is \(100 \Omega\).