Question

A heart defibrillator passes \(10.0{\rm{ }}A\) through a patient’s torso for \(5.00{\rm{ }}ms\) in an attempt to restore normal beating.

(a) How much charge passed?

(b) What voltage was applied if \(500{\rm{ }}J\) of energy was dissipated?

(c) What was the path’s resistance?

(d) Find the temperature increase caused in the \(8.00{\rm{ }}kg\) of affected tissue.

Short answer

1. Passing through patient's torso the charge is obtained as: \(q{\rm{ }} = {\rm{ }}50.0{\rm{ }}mC\).
2. To the patient the voltage applied is obtained as: \(\Delta V{\rm{ }} = {\rm{ }}10.0{\rm{ }}kV\).
3. The resistance of the path is obtained as: \(R{\rm{ }} = {\rm{ }}1.00{\rm{ }}k\Omega \).
4. Caused in the affected tissue the temperature increased is obtained as: \(\Delta T{\rm{ }} = {\rm{ }}1.79{\rm{ }} \times {\rm{ }}{10^{ - 2{\rm{ }}o}}{\rm{ }}C\).

Step-by-step solution

Define Resistance

Resistance is a measurement of the resistance to current flow in an electrical circuit. Resistance in ohms is denoted by the Greek letter omega\({\rm{(\Omega )}}\) .

Concepts and Principles

Electric current is the magnitude of the physical quantity of electric current\({\rm{I}}\)in a wire which equals the magnitude of the electric charge\(q\)that passes through a cross-section of the wire divided by the time interval\(\Delta t\)needed for that charge to pass:

\(I{\rm{ }} = {\rm{ }}\frac{{|q|}}{{\Delta t}}\)……………..(I)

The unit of current is the ampere\(A\), which is equivalent to one coulomb per second\((C/s)\).A current of\(1A\)(one ampere, or amp) means that\(1{\rm{ }}C\)of charge passes through a cross-section of the wire every second. The direction of the current is from higher to lower potential. So, it is in the direction that positive charges that would move.

The power of a process is the amount of some type of energy converted into a different type divided by the time interval\(\Delta t\)in which the process occurred:

\(P{\rm{ }} = {\rm{ }}\frac{{\Delta E}}{{\Delta t}}\)…………….(II)

If a potential difference\(\Delta V\)is maintained across a circuit element, the power, or the rate at which energy is supplied to the element, is:

\(P{\rm{ }} = {\rm{ }}I\Delta V\)………….(III)