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Chapter 26: Problem 26

If you touch the terminal of a battery, the small area of contact means that the skin resistance will be relatively large; \(50 \mathrm{k} \Omega\) is a reasonable value. What current will pass through your body if you touch the two terminals of a \(9.0 \mathrm{V}\) battery with your two hands? Will you feel it? Will it be dangerous?

Short Answer

Expert verified
The current that will pass through your body when you touch the two terminals of a 9.0V battery is about 0.18 mA, which is not typically dangerous but can be felt.

Step by step solution

01

- Understand the Given Information

From the problem, we're told the voltage from the battery is 9.0 Volts and the resistance in your body when touching the terminal of a battery is estimated to be 50 k惟. This resistance converts to 50000 惟.
02

- Apply Ohm's Law

Use Ohm's Law which states that current equals voltage divided by resistance. Rearrange the equation to solve for the current, \(I=V/R\). Substitute the given values into the equation to find the current, thus \(I=9.0/50000=0.00018 A\) or 0.18 mA.
03

- Analyze the Result

An electric shock with an electrical current of about 1 mA can be felt but is not typically dangerous. In this instance, the current going through the body will be 0.18 mA when the two terminals of a 9.0V battery are touched, which is less than 1 mA, therefore it can be felt but is not dangerous.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Electric Current
Electric current refers to the flow of electric charge in a circuit. It is one of the fundamental concepts in electricity and is typically measured in amperes (A). Electric current can be thought of as similar to water flowing through a pipe. In a circuit, these electric charges are carried by electrons flowing through a conductor, such as a wire.
  • Electric current is the rate of flow of electric charge.
  • It is driven by a difference in voltage between two points.
  • In calculations, it is represented as 'I' and calculated using Ohm's Law: \(I = \frac{V}{R}\).
In the given exercise, when touching the terminals of a battery, the electric current through your body is the result of the voltage of the battery divided by your body's resistance. This current is relatively small given the high resistance of human skin.
Concept of Skin Resistance
Skin resistance is an important factor when considering the flow of current through the human body. Resistance is a measure of how much a material opposes the flow of electric current. Human skin has a naturally high resistance, which acts as a protective barrier against electric currents.
  • Skin resistance is typically measured in ohms (\(\Omega\)).
  • Dry skin has higher resistance compared to wet skin.
  • It provides a protective barrier, reducing the risk of harm from low-level electric shocks.
In the example, the given skin resistance is 50 k\(\Omega\), which is quite a high value and greatly limits the amount of current that can flow through the body from a low voltage source, like a 9.0V battery. This high resistance reduces the danger from typical household batteries.
Explaining Voltage
Voltage, often referred to as electrical potential difference, is the force that pushes electric current through a circuit. It is measured in volts (V) and can be thought of as similar to pressure in a water system. Voltage establishes the potential energy needed to move charges across a circuit.
  • Voltage is what drives current through a resistance.
  • The higher the voltage, the more potential there is for electric current to flow.
  • In calculations, it is often denoted as 'V'.
In this exercise, the battery provides a 9.0V potential difference. This is fairly low when compared to mains electricity. When considering potential electrical hazards, the combination of voltage and current must be small enough to not overcome the natural resistance of the human body. With a 9.0V battery, the voltage is insufficient to push a dangerous current through the high resistance of dry skin.

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Most popular questions from this chapter

II The "power cube" transformer for a portable CD player has an output of \(4.5 \mathrm{V}\) and \(600 \mathrm{mA}\) (both rms) when plugged into a \(120 \mathrm{V}\) outlet. a. If the primary coil has 400 turns of wire, how many turns are on the secondary coil? b. What is the peak current in the primary coil?

An electronics hobbyist is building a radio set to receive the AM band, with frequencies from \(520 \mathrm{kHz}\) to \(1700 \mathrm{kHz}\). The antenna, which also serves as the inductor in an \(L C\) circuit, has an inductance of \(230 \mu \mathrm{H.}\) She needs to add a variable capacitor whose capacitance she can adjust to tune the radio. What is the minimum capacitance the capacitor must have? The maximum value?

The girl in Figure 26.12 of the chapter has her hand on the sphere of a Van de Graaff generator that is at a potential of \(400,000 \mathrm{V}\). She is standing on an insulating platform, so no current flows through her. But what happens if she touches something that is grounded? Is she still safe? Figure \(P 26.57\) shows the equivalent circuit. \(C_{\mathrm{VDG}}=20 \mathrm{pF}\) represents the capacitance of the Van de Graaff sphere, \(C_{\text {girl }}=100 \mathrm{pF}\) is the capacitance of the girl's body, and \(R=5 \mathrm{k} \Omega\) is the resistance of her body, from one hand to the other. The switch is closed when she touches ground. What is the initial current at the instant the switch is closed? b. What is the time constant for the current to decay? c. Occupational safety experts have found that a shock is safe if the product of the voltage, the current, and the time the current is delivered is less than \(13.5 \mathrm{V} \cdot \mathrm{A} \cdot \mathrm{s}=13.5 \mathrm{J}\) (see Problem 26.28). Estimate this product. Is this shock safe?

II The following appliances are connected to a single \(120 \mathrm{V}\), 15 A circuit in a kitchen: a 330 W blender, a 1000 W coffeepot, a \(150 \mathrm{W}\) coffee grinder, and a \(750 \mathrm{W}\) microwave oven. If these are all turned on at the same time, will they trip the circuit breaker?

A toaster oven is rated at \(1600 \mathrm{W}\) for operation at \(120 \mathrm{V}, 60 \mathrm{Hz}\). a. What is the resistance of the oven heater element? b. What is the peak current through it? c. What is the peak power dissipated by the oven?
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