### Understanding Series Circuits: Example Problem**Problem Statement:**Continuing with the same setup as above, where you connect a 6 Ω resistor and a 12 Ω resistor in series to a 9 V battery. Find the potential difference, \( V_1 \), across the 6 Ω resistor in Volts.**Hint: \( V_{Tot} = V_1 + V_2 \)**### Circuit Diagram Explanation:#### Components:1. **Resistor 1 (R1)**: 6 Ω2. **Resistor 2 (R2)**: 12 Ω3. **Battery (BAT1)**: 9 V#### Diagram:- The circuit diagram shows the 6 Ω resistor (R1) and the 12 Ω resistor (R2) connected in series with a 9 V battery.- The total circuit resistance (R_Tot) is the sum of R1 and R2.- The total current (I_Tot) flows through the circuit.**Diagram Analysis:**1. **Resistors in Series**: - When resistors are connected in series, their resistances add up. - \( R_{Tot} = R_1 + R_2 = 6 Ω + 12 Ω = 18 Ω \)2. **Current Calculation**: - Ohm's Law: \( V = IR \) - \( I_{Tot} = \frac{V_{BAT1}}{R_{Tot}} = \frac{9 V}{18 Ω} = 0.5 A \)3. **Voltage Drop Across Each Resistor**: - \( V_1 = I_{Tot} \times R_1 \) - \( V_1 = 0.5 A \times 6 Ω = 3 V \) - \( V_2 = I_{Tot} \times R_2 \) - \( V_2 = 0.5 A \times 12 Ω = 6 V \)Thus, the potential difference \( V_1 \) across the 6 Ω resistor is **3 Volts**.### SummaryIn a series circuit, the voltage drop across a resistor can be found using Ohm's Law. By knowing the total voltage and the resistance values, we can determine the current in the circuit and subsequently the voltage drop across each resistor. For the given problem, **Electric Circuits: Series and Parallel Resistances**In this section, we will explore the fundamental principles governing series and parallel circuits. These equations are critical for understanding how different configurations of resistors affect the overall resistance, current, and voltage in electrical circuits.**Basic Ohm's Law Relationships:**- \( V = IR \)- \( I = \frac{V}{R} \)- \( R = \frac{V}{I} \)**Series Circuits:**1. **Total Current (\( I_{Tot} \)):** - \( I_{Tot} = I_1 = I_2 = I_3 \); - In a series circuit, the current is the same through all components.2. **Total Voltage (\( V_{Tot} \)):** - \( V_{Tot} = V_1 + V_2 \);3. **Total Resistance (\( R_{Tot} \)):** - \( R_{Tot} = R_1 + R_2 \);**Parallel Circuits:**1. **Total Current (\( I_{Tot} \)):** - \( I_{Tot} = I_1 + I_2 \); - In a parallel circuit, the total current is the sum of the currents through each component.2. **Total Voltage (\( V_{Tot} \)):** - \( V_{Tot} = V_1 = V_2 = V_3 \); - In a parallel circuit, the voltage is the same across all components.3. **Total Resistance (\( R_{Tot} \)):** - \( \frac{1}{R_{Tot}} = \frac{1}{R_1} + \frac{1}{R_2} \); - The reciprocal of the total resistance is the sum of the reciprocals of the individual resistances.These principles are essential for analyzing and designing electrical circuits and are widely used in various applications ranging from simple electronic devices to complex electrical networks.

Ohm's law: This law states that the current is directly proportional to the voltage and inversely…

Continuing with the same setup as above, where you connect a 6Q resistor and a 12 Q resistor in series to a 9 V battery. Find the potential difference, V1, across the 6 resistor in Volis Hint: VTot = V1 = V2. RTot ITot BAT1 R2 12 Q R1 9 V

Continuing with the same setup as above, where you connect a 6Q resistor and a 12 Q resistor in series to a 9 V battery. Find the potential difference, V1, across the 6 resistor in Volis Hint: VTot = V1 = V2. RTot ITot BAT1 R2 12 Q R1 9 V

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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