### Educational Content: Circuit Analysis Problem#### Problem Description(a) In the figure, what value must $ R $ have if the current in the circuit is to be $ 1.3 \, \text{mA} $? Take $ \mathcal{E}_1 = 2.7 \, \text{V} $, $ \mathcal{E}_2 = 5.3 \, \text{V} $, and $ r_1 = r_2 = 3.9 \, \Omega $. (b) What is the rate at which thermal energy appears in $ R $?#### Instructional DiagramThe diagram shows a circuit with two voltage sources ($ \mathcal{E}_1 $ and $ \mathcal{E}_2 $) and their respective internal resistances ($ r_1 $ and $ r_2 $). Both sources are connected in series with an additional resistor $ R $. #### Diagram Details- **$ \mathcal{E}_1 $**: Voltage source 1, $ 2.7 \, \text{V} $- **$ \mathcal{E}_2 $**: Voltage source 2, $ 5.3 \, \text{V} $- **$ r_1 $**: Internal resistance of source 1, $ 3.9 \, \Omega $- **$ r_2 $**: Internal resistance of source 2, $ 3.9 \, \Omega $- **$ R $**: Resistor $ R $ (unknown)- Current in the circuit: $ 1.3 \, \text{mA} $#### Questions1. **(a):** Determine the value of resistor $ R $ in ohms ($\Omega$).2. **(b):** Calculate the rate at which thermal energy appears in resistor $ R $.#### Answer Inputs(a) - **Number** [Input box]- **Units** [Drop-down menu](b)- **Number** [Input box]- **Units** [Drop-down menu]This educational content aims to help students understand how to analyze simple circuits with series components and calculate relevant electrical properties. Use Ohm's Law and series resistor rules to solve these problems.

Answered: Image /qna-images/answer/ff948dad-c82c-4f06-a832-d1171b317d1b.jpg

(a) In the figure what value must R have if the current in the circuit is to be 1.3 mA? Take ₁ = 2.7 V, 8₂ = 5.3 V, and r₁ r₂ = 3.9 0. (b I What is the rate at which thermal energy appears in R? www.i R (a) Number IN -18₂ ww (b) Number i N Units Units >

(a) In the figure what value must R have if the current in the circuit is to be 1.3 mA? Take ₁ = 2.7 V, 8₂ = 5.3 V, and r₁ r₂ = 3.9 0. (b I What is the rate at which thermal energy appears in R? www.i R (a) Number IN -18₂ ww (b) Number i N Units Units >

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Ohm's law

Ohm’s law is a prominent concept in physics and electronics. It gives the relation between the current and the voltage. It is used to analyze and construct electrical circuits. Ohm's law states that the voltage across a conductor is directly proportional to the current flowing through it.

Path of Least Resistance

In a series of alternate pathways, the direction of least resistance is the actual or metaphorical route that offers the least resistance to forwarding motion by a given individual or body.

Question

### Educational Content: Circuit Analysis Problem

#### Problem Description
(a) In the figure, what value must $ R $ have if the current in the circuit is to be $ 1.3 \, \text{mA} $? Take $ \mathcal{E}_1 = 2.7 \, \text{V} $, $ \mathcal{E}_2 = 5.3 \, \text{V} $, and $ r_1 = r_2 = 3.9 \, \Omega $.

(b) What is the rate at which thermal energy appears in $ R $?

#### Instructional Diagram
The diagram shows a circuit with two voltage sources ($ \mathcal{E}_1 $ and $ \mathcal{E}_2 $) and their respective internal resistances ($ r_1 $ and $ r_2 $). Both sources are connected in series with an additional resistor $ R $.

#### Diagram Details
- **$ \mathcal{E}_1 $**: Voltage source 1, $ 2.7 \, \text{V} $
- **$ \mathcal{E}_2 $**: Voltage source 2, $ 5.3 \, \text{V} $
- **$ r_1 $**: Internal resistance of source 1, $ 3.9 \, \Omega $
- **$ r_2 $**: Internal resistance of source 2, $ 3.9 \, \Omega $
- **$ R $**: Resistor $ R $ (unknown)
- Current in the circuit: $ 1.3 \, \text{mA} $

#### Questions
1. **(a):** Determine the value of resistor $ R $ in ohms ($\Omega$).
2. **(b):** Calculate the rate at which thermal energy appears in resistor $ R $.

#### Answer Inputs
(a)
- **Number** [Input box]
- **Units** [Drop-down menu]

(b)
- **Number** [Input box]
- **Units** [Drop-down menu]

This educational content aims to help students understand how to analyze simple circuits with series components and calculate relevant electrical properties. Use Ohm's Law and series resistor rules to solve these problems.

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