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Part I: Battery capacity (typically given in A·h, "amp hours") is the finite amount of charge stored in a battery. If the load resistance is varied over time such that the current out of the battery is i(t) = io exp (−t/t), what is the total reduction in capacity to the battery after a "very long" time?

Part I: Battery capacity (typically given in A·h, "amp hours") is the finite amount of charge stored in a battery. If the load resistance is varied over time such that the current out of the battery is i(t) = io exp (−t/t), what is the total reduction in capacity to the battery after a "very long" time?

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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part I please

Problem 4: The circuit below is a common configuration that can be used to determine the value of a resistor, Rx. This is usually achieved by prescribing values for the R1 and R2 resistors, and then using an adjustable resistor (i.e., a "potentiometer") for R3. When the resistors are properly balanced, one could connect a resistor across the bridge at the points indicated by arrows and no current would flow across the resistor. Complete parts A - I. R₁ V₂ R₂ R3 Rx Part A: Using the passive sign convention, make reference marks on the circuit (current directions and polarity symbols). Where needed, assign circuit variables to the elements. Indicate nodes (A,B,C, ...) and a ground that you would use for nodal analysis. Indicate meshes that you would use for mesh analysis. Part B: Suppose you want to determine the voltages across R3 and Rx very quickly. Briefly explain how this can be done by inspection (i.e., without formal analyses like nodal or mesh) by exploiting the circuit structure and indicate which features allow you to do this. (i.e., the solution by inspection, not a system of equations) Part C: Using your method, write down the voltages across R3 and Rx in terms of the circuit resistances and the battery voltage. Part D: Suppose you wanted to balance the circuit, what potential difference must exist between the two indicated points? Part E: Using your previous answers, derive the value of Rx that balances the circuit in terms of the remaining resistances. Part F: Confirm your answer by deriving the value of Rx with node-voltage analysis (i.e. from scratch). Part G: Confirm your answer by deriving the value of Rx with mesh-current analysis (i.e. from scratch). Part H: Suppose you intentionally imbalance the circuit and then you connect a light bulb across the indicated points (model this as a load resistance, RL). Suppose also that yo ground the end of RL that is connected between R2 and Rx (use this instead of the ground you used previously). If you wish to use node-voltage analysis, what modification will you need to make? Write down the equations associated with the modification to the nodal analysis approach. (You do not need to write equations for the whole circuit or solve. Just write the equations for the modification.) Part I: Battery capacity (typically given in A-h, "amp hours") is the finite amount of charge stored in a battery. If the load resistance is varied over time such that the current out of the battery is i(t) = io exp (-t/t), what is the total reduction in capacity to the battery after a "very long" time?
Transcribed Image Text:Problem 4: The circuit below is a common configuration that can be used to determine the value of a resistor, Rx. This is usually achieved by prescribing values for the R1 and R2 resistors, and then using an adjustable resistor (i.e., a "potentiometer") for R3. When the resistors are properly balanced, one could connect a resistor across the bridge at the points indicated by arrows and no current would flow across the resistor. Complete parts A - I. R₁ V₂ R₂ R3 Rx Part A: Using the passive sign convention, make reference marks on the circuit (current directions and polarity symbols). Where needed, assign circuit variables to the elements. Indicate nodes (A,B,C, ...) and a ground that you would use for nodal analysis. Indicate meshes that you would use for mesh analysis. Part B: Suppose you want to determine the voltages across R3 and Rx very quickly. Briefly explain how this can be done by inspection (i.e., without formal analyses like nodal or mesh) by exploiting the circuit structure and indicate which features allow you to do this. (i.e., the solution by inspection, not a system of equations) Part C: Using your method, write down the voltages across R3 and Rx in terms of the circuit resistances and the battery voltage. Part D: Suppose you wanted to balance the circuit, what potential difference must exist between the two indicated points? Part E: Using your previous answers, derive the value of Rx that balances the circuit in terms of the remaining resistances. Part F: Confirm your answer by deriving the value of Rx with node-voltage analysis (i.e. from scratch). Part G: Confirm your answer by deriving the value of Rx with mesh-current analysis (i.e. from scratch). Part H: Suppose you intentionally imbalance the circuit and then you connect a light bulb across the indicated points (model this as a load resistance, RL). Suppose also that yo ground the end of RL that is connected between R2 and Rx (use this instead of the ground you used previously). If you wish to use node-voltage analysis, what modification will you need to make? Write down the equations associated with the modification to the nodal analysis approach. (You do not need to write equations for the whole circuit or solve. Just write the equations for the modification.) Part I: Battery capacity (typically given in A-h, "amp hours") is the finite amount of charge stored in a battery. If the load resistance is varied over time such that the current out of the battery is i(t) = io exp (-t/t), what is the total reduction in capacity to the battery after a "very long" time?
Expert Solution
Step 1

Given data

The expression for the current out of the battery is given by,

i=i0e-tτ

We need to calculate the total reduction in capacity to the battery after a very long time.

 

 

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