### Series-Parallel Circuit Analysis**Objective:**To analyze a circuit consisting of a 9.0 V battery connected to three resistors, and to carry out the following tasks:a. Draw the equivalent simplified circuit diagram.b. Determine the current drawn from the battery.c. Calculate the voltage across and the current through each resistor, and present the values in a table.**Circuit Description:**The circuit consists of three resistors:1. \( R1 = 50 \Omega \)2. \( R2 = 100 \Omega \)3. \( R3 = 75 \Omega \)**Diagram Analysis:**The provided circuit diagram shows the 9.0 V battery connected to a combination of resistors arranged in a mixed series-parallel configuration.- Resistor \( R1 \) and \( R2 \) are arranged in parallel.- The combination of \( R1 \) and \( R2 \) is then connected in series with \( R3 \).#### a. Simplified Circuit DiagramTo simplify the circuit:1. Calculate the equivalent resistance \( R_{12} \) of the parallel combination of \( R1 \) and \( R2 \):\[\frac{1}{R_{12}} = \frac{1}{R1} + \frac{1}{R2}\]\[\frac{1}{R_{12}} = \frac{1}{50 \Omega} + \frac{1}{100 \Omega}\]\[R_{12} = \left( \frac{1}{\frac{1}{50} + \frac{1}{100}} \right) \Omega\]\[R_{12} = \left( \frac{1}{0.03} \right) \Omega = 33.33 \Omega\]2. The equivalent resistance (\( R_{Total} \)) for the entire circuit, which is \( R_{12} \) in series with \( R3 \):\[R_{Total} = R_{12} + R3 = 33.33 \Omega + 75 \Omega = 108.33 \Omega\]#### b. Current Drawn from the BatteryUsing Ohm's Law:\[I = \frac{V}{R_{Total}}\]\[I = \frac{9.0 V}{

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A 9.0 V battery is connected to three resistors as shown in the figure below with R₁ = 502, R₂ 100 , and R3 = 75 Q = a. Draw the equivalent simplified circuit diagram. b. Determine the current drawn from the battery. C. With the value of current from the battery, find the voltage across and current through each resistor. Enter the values in a table 9.0 V 50 Ω 100 Ω www ww 75 02

A 9.0 V battery is connected to three resistors as shown in the figure below with R₁ = 502, R₂ 100 , and R3 = 75 Q = a. Draw the equivalent simplified circuit diagram. b. Determine the current drawn from the battery. C. With the value of current from the battery, find the voltage across and current through each resistor. Enter the values in a table 9.0 V 50 Ω 100 Ω www ww 75 02

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter10: Direct-current Circuits

Section: Chapter Questions

Problem 72AP: The rather simple circuit shown below is known as a voltage divider. The symbol consisting of three...

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