3. Two Resistances R1 = 3 N and R2 = 6 N are connected in series with an ideal battery supplying a voltage of AV = 9 Volts. (a) Sketch this circuit diagra (b) Calculate the total resistance and current.

College Physics
1st Edition
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:Paul Peter Urone, Roger Hinrichs
Chapter20: Electric Current, Resistance, And Ohm's Law
Section: Chapter Questions
Problem 52PE: What would be the maximum cost of a CFL such that the total cost (investment plus operating) would...
icon
Related questions
Question
### Problem Statement

3. Two resistances \( R_1 = 3 \, \Omega \) and \( R_2 = 6 \, \Omega \) are connected in series with an ideal battery supplying a voltage of \( \Delta V = 9 \) Volts.
   - (a) Sketch this circuit diagram.
   - (b) Calculate the total resistance and current.

### Instructions

**(a) Circuit Diagram Sketch:**

To sketch the circuit diagram:
1. Draw a battery symbol with a label indicating it supplies 9 Volts.
2. Connect a resistor labeled \( R_1 = 3 \, \Omega \) in series with the battery.
3. Connect a second resistor labeled \( R_2 = 6 \, \Omega \) in series with \( R_1 \).

**(b) Calculation of Total Resistance and Current:**

1. **Total Resistance (\(R_{\text{total}}\)):**
   - Formula: \( R_{\text{total}} = R_1 + R_2 \)
   - Calculation: \( R_{\text{total}} = 3 \, \Omega + 6 \, \Omega = 9 \, \Omega \)

2. **Current (\(I\)) Using Ohm’s Law:**
   - Formula: \( I = \frac{\Delta V}{R_{\text{total}}} \)
   - Calculation: \( I = \frac{9 \, \text{V}}{9 \, \Omega} = 1 \, \text{A} \)

### Explanation

In a series circuit, the total resistance is simply the sum of the individual resistances. The current flowing through the circuit can be determined by Ohm’s Law, where voltage divided by resistance gives the current.
Transcribed Image Text:### Problem Statement 3. Two resistances \( R_1 = 3 \, \Omega \) and \( R_2 = 6 \, \Omega \) are connected in series with an ideal battery supplying a voltage of \( \Delta V = 9 \) Volts. - (a) Sketch this circuit diagram. - (b) Calculate the total resistance and current. ### Instructions **(a) Circuit Diagram Sketch:** To sketch the circuit diagram: 1. Draw a battery symbol with a label indicating it supplies 9 Volts. 2. Connect a resistor labeled \( R_1 = 3 \, \Omega \) in series with the battery. 3. Connect a second resistor labeled \( R_2 = 6 \, \Omega \) in series with \( R_1 \). **(b) Calculation of Total Resistance and Current:** 1. **Total Resistance (\(R_{\text{total}}\)):** - Formula: \( R_{\text{total}} = R_1 + R_2 \) - Calculation: \( R_{\text{total}} = 3 \, \Omega + 6 \, \Omega = 9 \, \Omega \) 2. **Current (\(I\)) Using Ohm’s Law:** - Formula: \( I = \frac{\Delta V}{R_{\text{total}}} \) - Calculation: \( I = \frac{9 \, \text{V}}{9 \, \Omega} = 1 \, \text{A} \) ### Explanation In a series circuit, the total resistance is simply the sum of the individual resistances. The current flowing through the circuit can be determined by Ohm’s Law, where voltage divided by resistance gives the current.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781938168000
Author:
Paul Peter Urone, Roger Hinrichs
Publisher:
OpenStax College
Principles of Physics: A Calculus-Based Text
Principles of Physics: A Calculus-Based Text
Physics
ISBN:
9781133104261
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Physics for Scientists and Engineers with Modern …
Physics for Scientists and Engineers with Modern …
Physics
ISBN:
9781337553292
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
University Physics Volume 2
University Physics Volume 2
Physics
ISBN:
9781938168161
Author:
OpenStax
Publisher:
OpenStax
Physics for Scientists and Engineers, Technology …
Physics for Scientists and Engineers, Technology …
Physics
ISBN:
9781305116399
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning