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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

Expert verified
  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

01

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\({\rm{(\Omega )}}\).

02

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)

In Ohm's Law the current\(I\)through a circuit element (other than battery) can be determined by dividing the potential difference\(\Delta V\)across the circuit element by its resistance\(R\):

\(I{\rm{ }} = {\rm{ }}\frac{{\Delta V}}{R}\)………………(IV)

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Most popular questions from this chapter

If the 0.100mm diameter tungsten filament in a light bulb is to have a resistance of 0.200Ω at20.0°C, how long should it be?

What is the current when a typical static charge of \({\bf{0}}{\bf{.250}}\;{\bf{\mu C}}\) moves from your finger to a metal doorknob in \({\bf{1}}{\bf{.00}}\;{\bf{\mu s}}\) ?

(a) During surgery, a current as small as \(20.0\mu A\) applied directly to the heart may cause ventricular fibrillation. If the resistance of the exposed heart is \(300{\rm{ }}\Omega ,\)what is the smallest voltage that poses this danger? (b) Does your answer imply that special electrical safety precautions are needed?

(a) A defibrillator sends a \({\bf{6}}{\bf{.00}}\;{\bf{A}}\) current through the chest of a patient by applying a \({\bf{10000}}\;{\bf{V}}\) potential as in the figure below. What is the resistance of the path? (b) The defibrillator paddles make contact with the patient through a conducting gel that greatly reduces the path resistance. Discuss the difficulties that would ensue if a larger voltage were used to produce the same current through the patient, but with the path having perhaps 50 times the resistance. (Hint: The current must be about the same, so a higher voltage would imply greater power. Use the equation for power: \({\bf{P = }}{{\bf{I}}^{\bf{2}}}{\bf{R}}\).)

A resistor made of Nichrome wire is used in an application where its resistance cannot change more than\(1.00\;\% \)from its value at\({20.0^ \circ }\;{\rm{C}}\). Over what temperature range can it be used?

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