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R1 R2 a + S b

R1 R2 a + S b

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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The figure below shows a circuit that consists of two identical emf devices. If 

R1 = R2 = R

 and the switch is closed, find an expression (in terms of R and ) for the current I that is in the branch from point a to b. (To represent, use E.)

**Diagram Explanation:** The diagram represents an electrical circuit consisting of the following components: 1. **Batteries (Sources of Electromotive Force, EMF):** - There are two batteries in the circuit, each represented by the symbol \(\mathcal{E}\), which provide electrical energy to drive the current through the circuit. 2. **Resistors:** - Two resistors are present, labeled \(R_1\) and \(R_2\). Resistors impede the flow of current and are typically used to control and limit current within electrical circuits. 3. **Points \(a\) and \(b\):** - These are junction points in the circuit where the different circuit elements are connected. 4. **Current (\(I\)):** - The diagram shows a downward arrow between points \(a\) and \(b\), indicating the direction of current flow through that part of the circuit. 5. **Switch (\(S\)):** - The switch in the circuit is labeled \(S\). It is shown in the open position, meaning it breaks the circuit path, preventing current flow through the segment it's connected to. **Circuit Configuration:** - The circuit forms a closed loop with a main path consisting of the two resistors and the batteries. - The current \(I\) flows from the positive terminal of the left battery, through resistor \(R_1\), then through point \(a\) to point \(b\), continuing through the open switch \(S\) if closed, and finally back through \(R_2\) to the positive terminal of the right battery. **Conceptual Understanding:** - In this configuration, the switch \(S\) can control the current flow between points \(a\) and \(b\). When the switch is closed, current can flow through it; when open, the path is interrupted. - The resistors \(R_1\) and \(R_2\) will influence the total resistance and hence the current throughout the circuit according to Ohm's Law \(V = IR\). - Both batteries work together to provide the necessary voltage across the entire circuit.
Transcribed Image Text:**Diagram Explanation:** The diagram represents an electrical circuit consisting of the following components: 1. **Batteries (Sources of Electromotive Force, EMF):** - There are two batteries in the circuit, each represented by the symbol \(\mathcal{E}\), which provide electrical energy to drive the current through the circuit. 2. **Resistors:** - Two resistors are present, labeled \(R_1\) and \(R_2\). Resistors impede the flow of current and are typically used to control and limit current within electrical circuits. 3. **Points \(a\) and \(b\):** - These are junction points in the circuit where the different circuit elements are connected. 4. **Current (\(I\)):** - The diagram shows a downward arrow between points \(a\) and \(b\), indicating the direction of current flow through that part of the circuit. 5. **Switch (\(S\)):** - The switch in the circuit is labeled \(S\). It is shown in the open position, meaning it breaks the circuit path, preventing current flow through the segment it's connected to. **Circuit Configuration:** - The circuit forms a closed loop with a main path consisting of the two resistors and the batteries. - The current \(I\) flows from the positive terminal of the left battery, through resistor \(R_1\), then through point \(a\) to point \(b\), continuing through the open switch \(S\) if closed, and finally back through \(R_2\) to the positive terminal of the right battery. **Conceptual Understanding:** - In this configuration, the switch \(S\) can control the current flow between points \(a\) and \(b\). When the switch is closed, current can flow through it; when open, the path is interrupted. - The resistors \(R_1\) and \(R_2\) will influence the total resistance and hence the current throughout the circuit according to Ohm's Law \(V = IR\). - Both batteries work together to provide the necessary voltage across the entire circuit.
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