### Electrical Circuit Analysis - Example Problem**Problem Statement:**(a) In the figure, what value must \( R \) have if the current in the circuit is to be 1.3 mA? The given parameters are:- \( \mathcal{E}_1 = 2.7 \, \text{V} \)- \( \mathcal{E}_2 = 5.3 \, \text{V} \)- \( r_1 = r_2 = 3.9 \, \Omega \)(b) What is the rate at which thermal energy appears in \( R \)?**Diagram Analysis:**The provided image shows an electrical circuit with two voltage sources and three resistors. The circuit components are arranged in a combination of series and parallel as follows:1. \( \mathcal{E}_1 \) with an internal resistor \( r_1 \)2. \( \mathcal{E}_2 \) with an internal resistor \( r_2 \)3. An external resistor \( R \) in the circuit.The current flowing through the circuit is 1.3 mA.**Calculation Steps:**(a) To determine the value of \( R \):Using Ohm's Law and the rules for series circuits, we can calculate \( R \).The total voltage in the circuit \( V_{\text{total}} \) will be sum of \( \mathcal{E}_1 \) and \( \mathcal{E}_2 \).\[ V_{\text{total}} = \mathcal{E}_2 - \mathcal{E}_1 \]\[ V_{\text{total}} = 5.3 \text{ V} - 2.7 \text{ V} \]\[ V_{\text{total}} = 2.6 \text{ V} \]The total resistance \( R_{\text{total}} \) in the circuit is the sum of internal resistances and the external resistance \( R \):\[ R_{\text{total}} = r_1 + R + r_2 \]\[ R_{\text{total}} = 3.9 \, \Omega + R + 3.9 \, \Omega \]\[ R_{\text{total}} = 7.8 \, \Omega + R \]Using Ohm’s Law \( V = IR \):\[ R_{\text{total

Answered: Image /qna-images/answer/51c45328-b3db-45a4-866c-ac59506b514a.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 Q. (b) What is the rate at which thermal energy appears in R? ww www. (a) Number 1992.2 (b) Number i 2.6 Units Units Ω W <

(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 Q. (b) What is the rate at which thermal energy appears in R? ww www. (a) Number 1992.2 (b) Number i 2.6 Units Units Ω W <

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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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.

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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.

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### Electrical Circuit Analysis - Example Problem

**Problem Statement:**

(a) In the figure, what value must \( R \) have if the current in the circuit is to be 1.3 mA? The given parameters are:
- \( \mathcal{E}_1 = 2.7 \, \text{V} \)
- \( \mathcal{E}_2 = 5.3 \, \text{V} \)
- \( r_1 = r_2 = 3.9 \, \Omega \)

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

**Diagram Analysis:**
The provided image shows an electrical circuit with two voltage sources and three resistors. The circuit components are arranged in a combination of series and parallel as follows:

1. \( \mathcal{E}_1 \) with an internal resistor \( r_1 \)
2. \( \mathcal{E}_2 \) with an internal resistor \( r_2 \)
3. An external resistor \( R \) in the circuit.

The current flowing through the circuit is 1.3 mA.

**Calculation Steps:**

(a) To determine the value of \( R \):

Using Ohm's Law and the rules for series circuits, we can calculate \( R \).

The total voltage in the circuit \( V_{\text{total}} \) will be sum of \( \mathcal{E}_1 \) and \( \mathcal{E}_2 \).

\[ V_{\text{total}} = \mathcal{E}_2 - \mathcal{E}_1 \]
\[ V_{\text{total}} = 5.3 \text{ V} - 2.7 \text{ V} \]
\[ V_{\text{total}} = 2.6 \text{ V} \]

The total resistance \( R_{\text{total}} \) in the circuit is the sum of internal resistances and the external resistance \( R \):

\[ R_{\text{total}} = r_1 + R + r_2 \]
\[ R_{\text{total}} = 3.9 \, \Omega + R + 3.9 \, \Omega \]
\[ R_{\text{total}} = 7.8 \, \Omega + R \]

Using Ohm’s Law \( V = IR \):

\[ R_{\text{total

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