/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 42 The current in a \(47-\Omega\) r... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 20: Problem 42

The current in a \(47-\Omega\) resistor is 0.12 A. This resistor is in series with a \(28-\Omega\) resistor, and the series combination is connected across a battery. What is the battery voltage?

Short Answer

Expert verified
The battery voltage is 9 V.

Step by step solution

01

Understanding the Series Circuit

In a series circuit, the total resistance is the sum of the resistances of each component. The total resistance \(R_t\) can be calculated by adding the resistance of the \(47-\Omega\) resistor and the \(28-\Omega\) resistor: \(R_t = 47 + 28\).
02

Calculate Total Resistance

Calculate the total resistance: \(R_t = 47\, \Omega + 28\, \Omega = 75\, \Omega\).
03

Ohm's Law to Find Voltage

To find the battery voltage, apply Ohm's Law: \(V = IR\), where \(I\) is the current and \(R\) is the resistance. Use the current provided (0.12 A) and the total resistance (75 惟):\[ V = 0.12 \, A \times 75 \, \Omega \]
04

Calculate Battery Voltage

Substitute the values into Ohm's Law to find the battery voltage: \[ V = 0.12 \, A \times 75 \, \Omega = 9 \, V \]

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

Series Circuit
A series circuit is an electrical circuit in which components are connected end-to-end so that the same current flows through each component. This means:
  • The current is constant along all the components in a series.
  • The total voltage across the series circuit is the sum of the voltages across each component.
  • The total resistance is the sum of the resistances of all components.
For example, when you connect a 47-ohm resistor and a 28-ohm resistor in series, as given in the problem, they share the same current. The understanding of how components interact in a series path is crucial, particularly when calculating total resistance.
Total Resistance
Total resistance in a series circuit is an essential concept. It helps us determine how much the circuit will oppose the flow of electric current. Since a series circuit presents a single path for current, the total resistance is simply the sum of each resistor's resistance in the circuit. For instance:
  • With a 47-ohm resistor and a 28-ohm resistor in series, the total resistance is:
\[ R_t = 47 \, \Omega + 28 \, \Omega = 75 \, \Omega \]This formula is straightforward but powerful. By understanding how to effectively calculate total resistance, you set the groundwork for using other principles, such as Ohm's Law, to determine additional parameters like the total current or voltage.
Battery Voltage
Battery voltage in a series circuit can be calculated using Ohm's Law, which states: \[ V = I \times R \]This formula shows the relationship between voltage (V), current (I), and resistance (R). To find the voltage of the battery in this circuit, you multiply the total current by the total resistance:
  • Use the current provided: 0.12 A.
  • Use the total resistance: 75 惟 (as calculated from the series circuit).
  • Substitute these values into Ohm's Law:
\[ V = 0.12 \, A \times 75 \, \Omega = 9 \, V \]This calculation tells you that the battery must provide 9 volts to maintain a current of 0.12 A through the entire circuit. Understanding battery voltage helps in ensuring the proper functioning of the circuit and in selecting the right battery for your needs.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

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 \(\left(1.00 \mathrm{gal}=3.79 \times 10^{-3} \mathrm{~m}^{3}\right)\) 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 \((120 \mathrm{~V} \mathrm{ac}, 3.0 \Omega)\) to heat the water. Assuming that no heat is lost to the environment, determine the recovery time (in hours) of the unit.

A 60.0 -W lamp is placed in series with a resistor and a 120.0 -V source. If the voltage across the lamp is \(25 \mathrm{~V},\) what is the resistance \(R\) of the resistor?

There are approximately 110 million TVs in the United States. Each uses, on average, 75 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 the TVs turned on?

A blow-dryer and a vacuum cleaner each operate with a voltage of \(120 \mathrm{~V}\). The current rating of the blow-dryer is \(11 \mathrm{~A},\) and that of the vacuum cleaner is \(4.0 \mathrm{~A} .\) Determine the power consumed by (a) the blow-dryer and (b) the vacuum cleaner. (c) Determine the ratio of the energy used by the blow-dryer in 15 minutes to the energy used by the vacuum cleaner in one-half hour.

Two scales on a voltmeter measure voltages up to 20.0 and \(30.0 \mathrm{~V}\), respectively. The resistance connected in series with the galvanometer is \(1680 \Omega\) for the \(20.0-\mathrm{V}\) scale and \(2930 \Omega\) for the 30.0 - \(V\) scale. Determine the coil resistance and the full-scale current of the galvanometer that is used in the voltmeter.
See all solutions

Recommended explanations on Physics Textbooks

Work Energy and Power

Read Explanation

Wave Optics

Read Explanation

Physics of Motion

Read Explanation

Rotational Dynamics

Read Explanation

Solid State Physics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.