College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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Question

Apply the Loop Rule to ABHDA.

Use Kirchhoff’s junction rule and voltage/loop rule to find the current through each resistor in the following circuit: \(R_{AB} = 10 \, \Omega\), \(R_{BC} = 15 \, \Omega\), \(R_{AD} = 6 \, \Omega\), \(R_{CD} = 12 \, \Omega\), \(R_{G} = 4 \, \Omega\), and \(V_o = 10 \, \text{V}\).
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Transcribed Image Text:Use Kirchhoff’s junction rule and voltage/loop rule to find the current through each resistor in the following circuit: \(R_{AB} = 10 \, \Omega\), \(R_{BC} = 15 \, \Omega\), \(R_{AD} = 6 \, \Omega\), \(R_{CD} = 12 \, \Omega\), \(R_{G} = 4 \, \Omega\), and \(V_o = 10 \, \text{V}\).
The image depicts a Wheatstone bridge circuit, which is used to measure unknown electrical resistances. It consists of four resistors arranged in a diamond shape and a galvanometer. ### Explanation of the Diagram: - **Points and Resistors:** - **A, B, C, D:** These are the junction points of the circuit. - **\(R_{AB}\), \(R_{BC}\), \(R_{CD}\), \(R_{AD}\):** These are the resistors in the circuit. - **\(R_G\):** The resistor on the bridge between points B and D, connected through the galvanometer \(G\). - **Current Flow:** - **\(I_1\):** The current flowing from point A to point B. - **\(I_2\):** The current flowing from point A to point D. - **\(I_3\):** The current flowing through the galvanometer \(G\) from B to D. - Arrows indicate the direction of the current. - **Galvanometer (G):** - Located between points B and D, it measures the current flowing through \(R_G\). - **Voltage Source:** - \(V_0\) represents the potential difference across the circuit, with positive and negative terminals located at points F and K, respectively. ### Usage of Wheatstone Bridge: The Wheatstone bridge is balanced when \(I_3 = 0\), meaning no current flows through the galvanometer. This condition allows determination of the unknown resistor value by using the known values of the other resistors and the equation: \[ \frac{R_{AB}}{R_{BC}} = \frac{R_{AD}}{R_{CD}} \] This principle makes Wheatstone bridges essential tools in laboratories for precise resistance measurements.
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Transcribed Image Text:The image depicts a Wheatstone bridge circuit, which is used to measure unknown electrical resistances. It consists of four resistors arranged in a diamond shape and a galvanometer. ### Explanation of the Diagram: - **Points and Resistors:** - **A, B, C, D:** These are the junction points of the circuit. - **\(R_{AB}\), \(R_{BC}\), \(R_{CD}\), \(R_{AD}\):** These are the resistors in the circuit. - **\(R_G\):** The resistor on the bridge between points B and D, connected through the galvanometer \(G\). - **Current Flow:** - **\(I_1\):** The current flowing from point A to point B. - **\(I_2\):** The current flowing from point A to point D. - **\(I_3\):** The current flowing through the galvanometer \(G\) from B to D. - Arrows indicate the direction of the current. - **Galvanometer (G):** - Located between points B and D, it measures the current flowing through \(R_G\). - **Voltage Source:** - \(V_0\) represents the potential difference across the circuit, with positive and negative terminals located at points F and K, respectively. ### Usage of Wheatstone Bridge: The Wheatstone bridge is balanced when \(I_3 = 0\), meaning no current flows through the galvanometer. This condition allows determination of the unknown resistor value by using the known values of the other resistors and the equation: \[ \frac{R_{AB}}{R_{BC}} = \frac{R_{AD}}{R_{CD}} \] This principle makes Wheatstone bridges essential tools in laboratories for precise resistance measurements.
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