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A person standing barefoot on the ground \(20 \mathrm{m}\) from the point of a lightning strike experiences an instantaneous potential difference of 300 V between his feet. If we assume a skin resistance of \(1.0 \mathrm{k} \Omega,\) how much current goes up one leg and back down the other?

Short Answer

Expert verified
The amount of current that goes up one leg and back down the other is 0.3 A.

Step by step solution

01

Convert resistance to ohms

The resistance given is \(1.0 \, \mathrm{k} \Omega\), to convert kilo-ohms to ohms, multiply by 1000. Therefore, \(1.0 \, \mathrm{k} \Omega = 1.0 \times 1000 = 1000 \, \Omega\).
02

Apply Ohm’s law to find the current

Apply Ohm’s law formula which is \(I = V / R\). Here, \(V\) is 300V and \(R\) is 1000 \( \Omega\). Therefore, \(I = 300 / 1000 = 0.3 \, \mathrm{A}\).

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Key Concepts

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

Electric Current
Electric current is the flow of electric charge. In most cases, this flow consists of electrons moving through a conductor, like a wire, but it can also occur when charges move through the air, as in a lightning strike. The unit of electric current is the ampere, often abbreviated as "A".

An electric current is essential for transferring energy and powering various devices. It works similarly to the flow of water in pipes, where the water pressure pushes the liquid along. Here, the potential difference, or voltage, pushes the electric charge.

Let's break it down a bit further:
  • Electric current is measured using a device called an ammeter.
  • It is expressed in amperes, with smaller currents often given in milliamperes (mA), where 1 A = 1000 mA.
  • The current in a circuit depends on two main factors: the voltage applied and the resistance within the circuit.
Understanding electric current is key to grasping Ohm's law, which relates current, voltage, and resistance in an electrical circuit.
Resistance
Resistance is a term that describes how much a material opposes the flow of electric current. Every material has some resistance, just like water encountering obstacles in its path. Resistance is measured in ohms, denoted by the Greek letter omega (\(\Omega\)).

Here are a few important points to understand about resistance:
  • Materials with low resistance allow electric current to flow easily, similar to smooth pipes allowing water to flow freely.
  • Materials with high resistance require more voltage to push current through, similar to narrow or rough pipes restricting water flow.
  • In electronics, resistors are used intentionally to control the amount of current flowing in a circuit.
  • Resistance is often affected by temperature; typically, the higher the temperature, the higher the resistance, although there are exceptions.
In the context of Ohm's law, resistance determines how much current will flow when a specific potential difference is applied. It allows us to calculate the current using the formula \(I = \frac{V}{R}\), where \(I\) is the current, \(V\) is the voltage, and \(R\) is the resistance.
Potential Difference
Potential difference, commonly known as voltage, is what drives the electric current through a circuit. It represents the energy per unit charge that drives electric charges around a circuit. Voltage is measured in volts (V), and it can be thought of as the electric "pressure" that pushes the current.

Consider these points about potential difference:
  • A battery provides a potential difference, making it a power source for electronic devices.
  • Voltage can be compared to water pressure that pushes water through a hose: the higher the voltage, the greater the potential energy available to move the current.
  • When there's no potential difference, there's no current flow, similar to how water won't flow without pressure.
  • The potential difference between two points determines how much work is done in moving a charge between those points.
The potential difference is a crucial part of Ohm's law, which is expressed as \(V = IR\). This equation shows how voltage, current, and resistance are interrelated. Using this relationship, we can determine the current flowing through a resistance when a known potential difference is applied.

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Most popular questions from this chapter

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 voltage across a \(75 \mu \mathrm{H}\) inductor is described by the equation \(v_{\mathrm{L}}=(25 \mathrm{V}) \cos (60 t),\) where \(t\) is in seconds. a. What is the voltage across the inductor at \(t=0.10 \mathrm{s} ?\) b. What is the inductive reactance? c. What is the peak current?

If If you use an extension cord, current travels from the \(120 \mathrm{V}\) outlet, along one wire inside the cord, through the appliance you've plugged into the cord, and back to the outlet through a second wire in the cord. The total resistance of the two wires in a light-duty extension cord is \(0.40 \Omega ;\) the current through such a cord should be limited to 13 A. If a 13 A shop vacuum is powered using this cord, What is the voltage drop across the vacuum? b. How much power does the vacuum use? c. How much power is dissipated in the cord?

A \(2.0 \mathrm{mH}\) inductor is connected in parallel with a variable capacitor. The capacitor can be varied from \(100 \mathrm{pF}\) to \(200 \mathrm{pF}\). What is the range of oscillation frequencies for this circuit?

An \(R L C\) circuit consists of a \(48 \Omega\) resistor, a \(200 \mu \mathrm{F}\) capacitor, and an inductor. The rms current is \(2.5 \mathrm{A}\) when the circuit is connected to a \(120 \mathrm{V}, 60 \mathrm{Hz}\) outlet. What is the inductance?

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