### Potential Difference Across the 6 Ω ResistorContinuing 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, V1, across the 6 Ω resistor in Volts.**Hint:** VTot = V1 = V2.### Circuit Diagram ExplanationThe circuit diagram illustrates two resistors, R1 and R2, connected in series with a 9V battery (BAT1).- **R1 = 6 Ω**: The first resistor has a resistance of 6 Ohms.- **R2 = 12 Ω**: The second resistor has a resistance of 12 Ohms.- **BAT1 = 9 V**: The battery provides a potential difference of 9 Volts.The total resistance \( RTot \) is the sum of R1 and R2 because they are in series:\[ RTot = R1 + R2 \]\[ RTot = 6 \, \Omega + 12 \, \Omega \]\[ RTot = 18 \, \Omega \]The total current \( ITot \) through the series circuit can be found using Ohm's Law:\[ ITot = \frac{V_{Tot}}{R_{Tot}} \]\[ ITot = \frac{9 \, V}{18 \, \Omega} \]\[ ITot = 0.5 \, A \]The potential difference \( V1 \) across the 6 Ω resistor can be found by multiplying the current \( ITot \) by the resistance \( R1 \):\[ V1 = ITot \times R1 \]\[ V1 = 0.5 \, A \times 6 \, \Omega \]\[ V1 = 3 \, V \]Therefore, the potential difference across the 6 Ω resistor is \( 3 \, V \). ### Basic Electrical Equations and Concepts#### Ohm's Law:- \( V = IR \)- \( I = \frac{V}{R} \)- \( R = \frac{V}{I} \)### Series Circuits:- Total Current: \( I_{\text{Tot}} = I_1 = I_2 \)- Total Voltage: \( V_{\text{Tot}} = V_1 + V_2 \)- Total Resistance: \( R_{\text{Tot}} = R_1 + R_2 \)### Parallel Circuits:- Total Current: \( I_{\text{Tot}} = I_1 + I_2 \)- Total Voltage: \( V_{\text{Tot}} = V_1 = V_2 \)- Total Resistance:\[ \frac{1}{R_{\text{Tot}}} = \frac{1}{R_1} + \frac{1}{R_2} \]or\[ R_{\text{Tot}} = \frac{R_1 \cdot R_2}{R_1 + R_2} \]These equations provide the fundamental relationships between voltage (V), current (I), and resistance (R) in electrical circuits, both in series and parallel configurations. Understanding these relationships is crucial for analyzing and designing electrical circuits.

R1=6Ω; R2=12Ω; V=9V to find potential difference V1 across 6Ω resistor in volts

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 62 resistor in Volts. Hint: VTot = V1 = V2. RTot ITot +. R1 R2 BAT1 12Ω 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 62 resistor in Volts. Hint: VTot = V1 = V2. RTot ITot +. R1 R2 BAT1 12Ω 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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