Electric Circuits Legacy Problem #9 Guided Solution
Problem*
A stun gun or TASER is designed to put out a few seconds worth of electric pulses that impress a voltage of about 1200 V across the human body. This results in an average current of approximately 3 mA into a human body. Using these figures, estimate the resistance of the human body.
Audio Guided Solution
Precise numerical figures for stun guns or tasers are a little difficult to find for obvious reasons. It's not something that they generally experiment with. But it is generally estimated that the pulses from a stun gun might impress an electric potential difference across the human body with as much as 1,200 volts, and that this causes an estimated current of about 3 milliamps through the body. What we're asked to calculate here is the resistance of the human body based upon these estimated figures. So we have the equation that delta V, or electric potential difference in volts, is equal to the current in amperes multiplied by the resistance in ohms. That's delta V equals I times R. Here, delta V is 1,200 volts. And the I is 3 milliamps, but we'll need to convert that to units of amperes. There are 1,000 milliamps in 1 ampere, so we'll move the decimal place to the left three places such that the current is 0.003 amperes. So 1,200 volts equals 0.003 amps multiplied by resistance. We can solve for resistance and we'll get about 400,000 ohms of resistance, or 4 times 10 to the 5th ohms.
Solution
4x105 Ω
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record them in an organized manner. Equate given values to the symbols used to represent the corresponding quantity - e.g., \(\descriptive{\text{δV}}{δV,change in voltage} = 9.0\unit{\volt}\); \(\descriptive{R}{R,resistance} = 0.025\unit{\ohm}\); \(\descriptive{I}{I,current} = \colorbox{gray}{Unknown}\).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
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