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Chapter 20: Problem 111

In the Arctic, electric socks are useful. A pair of socks uses a \(9.0-\mathrm{V}\) battery pack for each sock. A current of \(0.11 \mathrm{A}\) is drawn from each battery pack by wire woven into the socks. Find the resistance of the wire in one sock.

Short Answer

Expert verified
The resistance is approximately 81.82 ohms.

Step by step solution

01

Identify the known values

We are given the voltage \( V = 9.0 \text{ V} \) and the current \( I = 0.11 \text{ A} \). These are the values provided in the problem statement.
02

Use Ohm's Law

Ohm's Law states that the voltage \( V \) across a resistor is equal to the current \( I \) flowing through it times the resistance \( R \). The formula is \( V = I \times R \).
03

Rearrange Ohm's Law to solve for resistance

To find resistance \( R \), rearrange the formula as follows: \( R = \frac{V}{I} \).
04

Substitute the known values into the formula

Substitute the known values into the rearranged formula: \( R = \frac{9.0 \text{ V}}{0.11 \text{ A}} \).
05

Calculate the resistance

Perform the division: \( R \approx 81.82 \text{ ohms} \). This is the resistance of the wire in one sock.

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Key Concepts

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

Resistance Calculation
Understanding how to calculate resistance is critical when working with electrical circuits. Resistance is a measure of how much a material opposes the flow of electric current. Ohm's law provides a simple formula to calculate resistance, which is symbolized by the letter
  • Resistance (R) is measured in ohms (鈩�).
  • It can be calculated using the formula: \( R = \frac{V}{I} \).
  • In this formula, \( V \) stands for voltage, and \( I \) for current.
Resistance affects how easily current can flow through a circuit. High resistance means less current can pass through. Remember, resistance depends on the material and thickness of the wire, among other factors.
Electric Current
Electric current is the flow of electric charge around a circuit. It is an essential part of any electrical system. To understand how current works, keep the following in mind:
  • Current is the rate at which charge flows through a point in the circuit.
  • It is measured in amperes, or amps (A).
  • Current is crucial for the functioning of electrical devices as it carries energy from one point to another.
Current flows in a closed loop, meaning it needs a path back to its source. In the context of Ohm's law, current plays a central role in determining how devices work within an electrical circuit.
Voltage
Voltage is the potential difference between two points in a circuit that drives current. It is an essential factor in how electrical circuits operate. Voltage can be thought of as the pressure pushing the current through the circuit.
  • Voltage is measured in volts (V).
  • It acts like the push or force that moves electric charges.
  • Higher voltage means more force to drive the current.
Understanding voltage helps us know how much energy is available to move electrons. In electrical devices, voltage determines how much work the current can do, affecting brightness, power, and more.

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Most popular questions from this chapter

An aluminum wire is hung between two towers and has a length of \(175 \mathrm{m} .\) A current of \(125 \mathrm{A}\) exists in the wire, and the potential difference between the ends of the wire is \(0.300 \mathrm{V} .\) The density of aluminum is \(2700 \mathrm{kg} / \mathrm{m}^{3} .\) Find the mass of the wire.

There are approximately 110 million households that use TVs in the United States. Each TV uses, on average, \(75 \mathrm{W}\) of power and is turned on for 6.0 hours a day. If electrical energy costs \(\$ 0.12\) per \(\mathrm{kWh}\), how much money is spent every day in keeping 110 million TVs turned on?

The recovery time of a hot water heater is the time required to heat all the water in the unit to the desired temperature. Suppose that a 52-gal \(\left(1.00\right.\) gal \(\left.=3.79 \times 10^{-3} \mathrm{m}^{3}\right)\) unit starts with cold water at \(11^{\circ} \mathrm{C}\) and delivers hot water at \(53^{\circ} \mathrm{C}\). The unit is electric and utilizes a resistance heater \((120 \mathrm{V}\) ac, \(3.0 \Omega\) ) to heat the water. Assuming that no heat is lost to the environment, determine the recovery time (in hours) of the unit.

The heating element in an iron has a resistance of \(24 \Omega .\) The iron is plugged into a \(120-\mathrm{V}\) outlet. What is the power delivered to the iron?

Two resistors, 42.0 and \(64.0 \Omega,\) are connected in parallel. The current through the \(64.0-\Omega\) resistor is \(3.00 \mathrm{A}\). (a) Determine the current in the other resistor. (b) What is the total power supplied to the two resistors?
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