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For a Wheatstone bridge with R1 = 432.1 Ω, R2 = 55.2 kΩ, and Rk = 6654.543 Ω, what is Rx ?   For a Wheatstone bridge with R2 /R1 = 55, and Rk = 300Ω, what is Rx ?

For a Wheatstone bridge with R1 = 432.1 Ω, R2 = 55.2 kΩ, and Rk = 6654.543 Ω, what is Rx ?   For a Wheatstone bridge with R2 /R1 = 55, and Rk = 300Ω, what is Rx ?

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College Physics
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ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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For a Wheatstone bridge with R1 = 432.1 Ω, R2 = 55.2 kΩ, and Rk = 6654.543 Ω, what is Rx ?

 

For a Wheatstone bridge with R2 /R1 = 55, and Rk = 300Ω, what is Rx ?

### Wheatstone Bridge Circuit Diagram The diagram illustrates a Wheatstone bridge circuit used for measuring unknown electrical resistances. The circuit is composed of four resistors, a galvanometer (G), and a power source providing voltage (\( V_o \)). #### Components and Connections: - **Points**: The circuit has four key junctions: A, B, C, and D. - **Resistors**: - \( R_1 \) is connected between junctions A and C. - \( R_2 \) is connected between junctions A and D. - \( R_k \) is connected between junctions C and B. - \( R_x \) (the unknown resistor) is connected between junctions D and B. - **Galvanometer (G)**: Connected between junctions A and B. It detects any current flowing through this branch. - **Current**: - \( I \) is the current supplied by the voltage source (\( V_o \)). - \( I_a \) is the current flowing from A to B through the galvanometer. - \( I_b \) is the current returning from B to A through the galvanometer in the opposite direction of \( I_a \). #### Functionality: The Wheatstone bridge is balanced when the ratio \( \frac{R_1}{R_k} = \frac{R_2}{R_x} \) holds true, at which point no current flows through the galvanometer (\( I_a = I_b = 0 \)). This balance condition allows the determination of the unknown resistance \( R_x \) when the other three resistances are known.
Transcribed Image Text:### Wheatstone Bridge Circuit Diagram The diagram illustrates a Wheatstone bridge circuit used for measuring unknown electrical resistances. The circuit is composed of four resistors, a galvanometer (G), and a power source providing voltage (\( V_o \)). #### Components and Connections: - **Points**: The circuit has four key junctions: A, B, C, and D. - **Resistors**: - \( R_1 \) is connected between junctions A and C. - \( R_2 \) is connected between junctions A and D. - \( R_k \) is connected between junctions C and B. - \( R_x \) (the unknown resistor) is connected between junctions D and B. - **Galvanometer (G)**: Connected between junctions A and B. It detects any current flowing through this branch. - **Current**: - \( I \) is the current supplied by the voltage source (\( V_o \)). - \( I_a \) is the current flowing from A to B through the galvanometer. - \( I_b \) is the current returning from B to A through the galvanometer in the opposite direction of \( I_a \). #### Functionality: The Wheatstone bridge is balanced when the ratio \( \frac{R_1}{R_k} = \frac{R_2}{R_x} \) holds true, at which point no current flows through the galvanometer (\( I_a = I_b = 0 \)). This balance condition allows the determination of the unknown resistance \( R_x \) when the other three resistances are known.
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