Question

If a defibrillator passes 15 A of current through a patient’s body for 0.1 seconds, how much charge goes through the patient’s skin? (A) 0.15 C (B) 1.5 C (C) 15 C (D) 150 C

Short answer

1.5 C

Step-by-step solution

Understand the relationship between current and charge

Current (\ref{I}) is the rate of flow of charge (\ref{Q}) over time (\ref{t}). The relationship can be expressed with the formula: \[ I = \frac{Q}{t} \]

Rearrange the formula to solve for charge

To find the charge (\ref{Q}), rearrange the formula: \[ Q = I \times t \] This shows that charge is equal to current multiplied by time.

Plug in the values given in the problem

We know the current (\ref{I}) is 15 A and the time (\ref{t}) is 0.1 seconds. Plug these values into the formula: \[ Q = 15 \text{ A} \times 0.1 \text{ s} \]

Calculate the charge

Multiplying the current by the time gives: \[ Q = 15 \times 0.1 = 1.5 \text{ C} \] This means the charge that goes through the patient's skin is 1.5 Coulombs.

Key concepts

Current and Charge Relationship

Current and charge are closely related in physics. Current, represented by the symbol I, is defined as the rate at which charge flows through a point in a circuit. Charge, symbolized as Q, is the actual quantity of electricity transported by the current. To understand this better, imagine water flowing through a pipe. The water flowing per second is like the current, and the total water that has flowed is like the charge.
The mathematical relationship between current and charge is given by the formula: \[ I = \frac{Q}{t} \] where I is the current, Q is the charge, and t is the time. This reveals that current is the amount of charge passing through a point per unit time.

Charge Calculation Formula

To calculate the charge when current and time are known, the formula can be rearranged. The rearranged version is: \[ Q = I \times t \] Here, you multiply the current (I) by the time (t) to find the charge (Q).
Let’s look at our specific example. The problem states that a current of 15 A passes through a patient's body for 0.1 seconds. Plugging these numbers into the formula, you get: \[ Q = 15 \text{ A} \times 0.1 \text{ s} \] When you multiply, the result is: \[ Q = 1.5 \text{ C} \] This means 1.5 Coulombs of charge passes through the patient's skin.

Defibrillator Physics

Defibrillators are lifesaving devices used to treat cardiac arrhythmias, including ventricular fibrillation. They work by delivering a dose of electric current (often called a 'shock') to the heart. This electric current variously aims to depolarize a critical mass of the heart muscle, thereby ending the arrhythmia and allowing the heart’s natural pacemaker to reestablish an effective rhythm.
The amount of charge delivered in a shock is vital. Too little charge, and the shock will be ineffective; too much, and it could cause damage or other complications. Hence, accurate calculations of charge, as seen in our example where 1.5 Coulombs pass through the patient's skin, are crucial in defibrillator operations.

Coulombs

In the context of electrical charge, the Coulomb (C) is the standard unit of measurement. Named after Charles-Augustin de Coulomb, this unit quantifies the amount of electric charge transferred by a steady current of one ampere in one second.
In simpler terms, 1 Coulomb equals the charge resulting from 1 ampere of current flowing for 1 second. Our calculation, resulting in a charge of 1.5 Coulombs, means that the defibrillator delivers the equivalent charge that would flow from a 1-ampere current running for 1.5 seconds, given that 1.5 seconds = 0.1 seconds at 15 amperes.
Understanding and using the Coulomb in calculations helps ensure precise measurements and effective treatments in electrical applications, particularly in medical devices like defibrillators.