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Problem 2: A lightbulb is in series with an R = 2.02 resistor. The lightbulb dissipates P = 10 W when this series circuit is con- nected to a AVbat = 9.0 V battery. What is the current through the lightbulb? a) In Fig.2, draw the diagram that represents this electric cir- cuit. A library of basic symbols used for electric circuit drawings is given in paragraph 28.1 of the textbook. b) Express the resistance of the lightbulb, Rub, in terms of the power that it dissipates, P, and the current in the circuit, I. Do not plug in the numerical values yet, just write down the formula. FIG. 2: The scheme for Problem 2 c) Write down the Kirchhoff's loop law for this circuit. This should result in a quadratic equation for the current I. Formulate this equation in a symbolic form (the coefficients must be some functions of AVbat, R and P). d) Plug in the numerical values of the parameters and solve the quadratic equation for I. You will get two possible values for the current. e) Naturally, the two values of I that you got in d) correspond to two different lightbulbs (a single lughtbulb of a fixed resistance uniquely determines the current in the circuit). What would be the two possible values of the rating (nominal) power of the lightbulbs that satisfy the conditions of the problem?

Problem 2: A lightbulb is in series with an R = 2.02 resistor. The lightbulb dissipates P = 10 W when this series circuit is con- nected to a AVbat = 9.0 V battery. What is the current through the lightbulb? a) In Fig.2, draw the diagram that represents this electric cir- cuit. A library of basic symbols used for electric circuit drawings is given in paragraph 28.1 of the textbook. b) Express the resistance of the lightbulb, Rub, in terms of the power that it dissipates, P, and the current in the circuit, I. Do not plug in the numerical values yet, just write down the formula. FIG. 2: The scheme for Problem 2 c) Write down the Kirchhoff's loop law for this circuit. This should result in a quadratic equation for the current I. Formulate this equation in a symbolic form (the coefficients must be some functions of AVbat, R and P). d) Plug in the numerical values of the parameters and solve the quadratic equation for I. You will get two possible values for the current. e) Naturally, the two values of I that you got in d) correspond to two different lightbulbs (a single lughtbulb of a fixed resistance uniquely determines the current in the circuit). What would be the two possible values of the rating (nominal) power of the lightbulbs that satisfy the conditions of the problem?

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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Hello, can you help me with part d and part e because I don't understand is there any chance you can help me with part d and part e and also can you label them so I know which one is which 

**Problem 2:** A lightbulb is in series with an \( R = 2.0 \, \Omega \) resistor. The lightbulb dissipates \( P = 10 \, \text{W} \) when this series circuit is connected to a \( \Delta V_{\text{bat}} = 9.0 \, \text{V} \) battery. What is the current through the lightbulb? a) In Fig. 2, draw the diagram that represents this electric circuit. A library of basic symbols used for electric circuit drawings is given in paragraph 28.1 of the textbook. b) Express the resistance of the lightbulb, \( R_{\text{lb}} \), in terms of the power that it dissipates, \( P \), and the current in the circuit, \( I \). Do not plug in the numerical values yet, just write down the formula. c) Write down the Kirchhoff’s loop law for this circuit. This should result in a quadratic equation for the current \( I \). Formulate this equation in a symbolic form (the coefficients must be some functions of \( \Delta V_{\text{bat}}, R, \) and \( P \)). d) Plug in the numerical values of the parameters and solve the quadratic equation for \( I \). You will get two possible values for the current. e) Naturally, the two values of \( I \) that you got in d) correspond to two different lightbulbs (a single lightbulb of a fixed resistance uniquely determines the current in the circuit). What would be the two possible values of the rating (nominal) power of the lightbulbs that satisfy the conditions of the problem? --- **Explanation of Figure 2:** The figure labeled "Fig. 2: The scheme for Problem 2" presumably illustrates a series circuit containing a battery, a resistor, and a lightbulb. This diagram would typically show the battery symbol connected in series with the resistor and lightbulb, indicating the flow of current through these components. The battery likely has a positive and negative terminal, and the components are connected end-to-end in this order, forming a loop that represents the complete circuit path. Since the actual diagram is not provided textually, it is assumed to follow standard electrical schematic conventions.
Transcribed Image Text:**Problem 2:** A lightbulb is in series with an \( R = 2.0 \, \Omega \) resistor. The lightbulb dissipates \( P = 10 \, \text{W} \) when this series circuit is connected to a \( \Delta V_{\text{bat}} = 9.0 \, \text{V} \) battery. What is the current through the lightbulb? a) In Fig. 2, draw the diagram that represents this electric circuit. A library of basic symbols used for electric circuit drawings is given in paragraph 28.1 of the textbook. b) Express the resistance of the lightbulb, \( R_{\text{lb}} \), in terms of the power that it dissipates, \( P \), and the current in the circuit, \( I \). Do not plug in the numerical values yet, just write down the formula. c) Write down the Kirchhoff’s loop law for this circuit. This should result in a quadratic equation for the current \( I \). Formulate this equation in a symbolic form (the coefficients must be some functions of \( \Delta V_{\text{bat}}, R, \) and \( P \)). d) Plug in the numerical values of the parameters and solve the quadratic equation for \( I \). You will get two possible values for the current. e) Naturally, the two values of \( I \) that you got in d) correspond to two different lightbulbs (a single lightbulb of a fixed resistance uniquely determines the current in the circuit). What would be the two possible values of the rating (nominal) power of the lightbulbs that satisfy the conditions of the problem? --- **Explanation of Figure 2:** The figure labeled "Fig. 2: The scheme for Problem 2" presumably illustrates a series circuit containing a battery, a resistor, and a lightbulb. This diagram would typically show the battery symbol connected in series with the resistor and lightbulb, indicating the flow of current through these components. The battery likely has a positive and negative terminal, and the components are connected end-to-end in this order, forming a loop that represents the complete circuit path. Since the actual diagram is not provided textually, it is assumed to follow standard electrical schematic conventions.
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