Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 29, Problem 7SP

For the circuit shown in Fig. 29-6, find the current in the 0.96- Ω resistor and the terminal voltages of the batteries.

Chapter 29, Problem 7SP, 29.7 [II]	For the circuit shown in Fig. 29-6, find the current in the 0.96- resistor and the

Fig. 29-6

Expert Solution & Answer
Check Mark
To determine

The current in the 0.96 Ω resistor and the terminal voltage of the batteries in the circuit given in Fig.29-6.

Answer to Problem 7SP

Solution:

5.0 A, 4.8 V, and 4.8 V

Explanation of Solution

Given data:

Refer to the circuit given in Fig. 29-6.

Formula used:

Kirchhoff’s loop law: The algebraic sum of the potential change in a closed circuit is zero.

In a parallel combination, the voltage remains constant and the current is distributed. In a series combination, the current remains constant and the voltage is distributed.

Write the expression for potential difference from Ohm’s law.

V=IR

Here, R is the resistance of the resistor, V is the potential difference across the resistor, and I is the current through the resistor.

Explanation:

Consider the following circuit shown in Figure 1.

Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines), Chapter 29, Problem 7SP

Apply loop rule to the loop abcda yields, in volts.

(0.96)I1+(0.20)(I1I2)5.0=0(1.16)I1(0.20)I2=5.0 …… (1)

Apply loop rule to loop adefa yields, in volts.

(0.20)(I2I1)+5.0+(0.30)(I2)6.0=0(0.20)I1+(0.50)I2=1.0

Solve further for I1.

I2=1.0+(0.20)I1(0.50) …… (2)

Substitute 1.0 V+(0.20)I1(0.50) for I2 from equation (2) in equation (1)

(1.16)I1(0.20)(1.0+(0.20)I1(0.50))=5.0(1.16)I10.4(0.08)I1=5.0(1.08)I1=5.4I1=5.0

Thus, this yields that I1=5.0 A.

Therefore, the current in the 0.96 Ω resistor is 5.0 A.

Calculate the current I2.

Substitute 5.0 for I1 in equation (2)

I2=1.0+(0.20)(5.0)(0.50)=2.0(0.50)=4.0

Thus, this yields that I2=4.0 A.

Calculate the current flow in the branch ad in Figure 2.

Iad=I1I2=5.0 A4.0 A=1.0 A

The value of Iad is positive. Thus, the direction of the current in Iad is from point d to point a.

Calculate the terminal voltage of the battery, whose emf is ε1=6.0 V.

VT1=ε1I2r1

Substitute 6.0 V for ε1, 4.0 A for I2, and 0.30 Ω for r1

VT1=6.0 V(4.0 A)(0.30 Ω)=6.0 V1.2 V=4.8 V

Thus, the terminal voltage of the battery, whose emf ε1=6.0 V is 4.8 V.

Calculate the terminal voltage of the battery, whose emf is ε2=5.0 V.

VT2=ε2Iadr2

Substitute 5.0 V for ε2, 1.0 A for Iad, and 0.30 Ω for r1

VT2=6.0 V(4.0 A)(0.30 Ω)=6.0 V1.2 V=4.8 V

Thus, the terminal voltage of the battery, whose emf ε2=5.0 V is 4.8 V.

Conclusion:

Therefore, the current in the 0.96 Ω resistor is 5.0 A, the terminal voltage of the battery, whose emf ε1=6.0 V is 4.8 V, and the terminal voltage of the battery, whose emf ε2=5.0 V is 4.8 V.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
As shown in Fig. 28-2(a), a battery (internal resistance I 2) is connected in series with two resistors. Compute (a) the current in the circuit, (b) the p.d. across each resistor, and (c) the terminal p.d. of the battery. 6. E- 18 V r-12 -W- -W 122 (a) Fig. 28-2
When a R = 90.7 Q resistor is connected across a 12 V battery, a current of 124.2 mA flows. What is the internal resistance of the battery and Terminal voltage of the battery ? (a) internal resistance of the battery(in 2) = (b) Terminal voltage of the battery in V = %3D
Using as many 12 Ω resistors as you need, produce a resistor circuit whose equivalent resistance is:(a) 18 Ω(b) 30 Ω
Knowledge Booster
Background pattern image
Physics
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Ohm's law Explained; Author: ALL ABOUT ELECTRONICS;https://www.youtube.com/watch?v=PV8CMZZKrB4;License: Standard YouTube License, CC-BY