Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 20: Problem 30

A de motor is connected to a constant emf of \(12.0 \mathrm{V}\) The resistance of its windings is \(2.0 \Omega .\) At normal operating speed, the motor delivers \(6.0 \mathrm{W}\) of mechanical power. (a) What is the initial current drawn by the motor when it is first started up? (b) What current does it draw at normal operating speed? (c) What is the back emf induced in the windings at normal speed?

Short Answer

Expert verified
Answer: 11 V

Step by step solution

01

(Step 1: Calculate initial current)

(When the motor is first started, it does not have any back emf, so the total emf across the motor is equal to the emf applied (12 V). We can use Ohm's law, which relates voltage (V), current (I), and resistance (R), to find the initial current: I = V / R Substitute the given values: I_initial = (12 V) / (2 Ω) = 6 A The initial current drawn by the motor is 6 A.)
02

(Step 2: Calculate current at normal operating speed)

(We are given that at normal operating speed, the motor delivers 6 W of mechanical power. We can use the power formula mentioned earlier: Power = Voltage * Current or P = V * I We can rearrange the formula to solve for the current at normal operating speed: I_normal = Power / Voltage Substitute the known values: I_normal = (6 W) / (12 V) = 0.5 A The current drawn by the motor at normal operating speed is 0.5 A.)
03

(Step 3: Calculate back emf at normal operating speed)

(At normal operating speed, the back emf (E_back) opposes the applied emf (V). To find the back emf, we will use Kirchhoff's law, which states that the sum of the voltages around a closed loop in a circuit is equal to zero: V - E_back - I_normal * R = 0 Rearrange the equation to solve for E_back: E_back = V - I_normal * R Substitute the known values: E_back = 12 V - (0.5 A) * (2 Ω) = 12 V - 1 V = 11 V The back emf induced in the windings at normal operating speed is 11 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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

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

A horizontal desk surface measures \(1.3 \mathrm{m} \times 1.0 \mathrm{m} .\) If Earth's magnetic field has magnitude \(0.44 \mathrm{mT}\) and is directed \(65^{\circ}\) below the horizontal, what is the magnetic flux through the desk surface?
The primary coil of a transformer has 250 turns; the secondary coil has 1000 turns. An alternating current is sent through the primary coil. The emf in the primary is of amplitude \(16 \mathrm{V}\). What is the emf amplitude in the secondary? (tutorial: transformer)
Calculate the equivalent inductance \(L_{\mathrm{eq}}\) of two ideal inductors, \(L_{1}\) and \(L_{2},\) connected in parallel in a circuit. Assume that their mutual inductance is negligible. [Hint: Imagine replacing the two inductors with a single equivalent inductor \(L_{\mathrm{eq}} .\) How is the emf in the parallel equivalent related to the emfs in the two inductors? What about the currents? \(]\)
When the armature of an ac generator rotates at $15.0 \mathrm{rad} / \mathrm{s},\( the amplitude of the induced emf is \)27.0 \mathrm{V}$ What is the amplitude of the induced emf when the armature rotates at $10.0 \mathrm{rad} / \mathrm{s} ?$ (tutorial: generator)
Suppose you wanted to use Earth's magnetic field to make an ac generator at a location where the magnitude of the field is \(0.50 \mathrm{mT}\). Your coil has 1000.0 turns and a radius of \(5.0 \mathrm{cm} .\) At what angular velocity would you have to rotate it in order to generate an emf of amplitude $1.0 \mathrm{V} ?$
See all solutions

Recommended explanations on Physics Textbooks

Nuclear Physics

Read Explanation

Electrostatics

Read Explanation

Modern Physics

Read Explanation

Geometrical and Physical Optics

Read Explanation

Magnetism and Electromagnetic Induction

Read Explanation

Measurements

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.

Sign-up for free