Ch 28: Fundamentals of Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796당신이 사용하는 게 아니라요?교과서 변경

Knight Calc 5th Edition

Ch 28: Fundamentals of Circuits

문제 64b

28장, 문제 64b

A 12 V car battery dies not so much because its voltage drops but because chemical reactions increase its internal resistance. A good battery connected with jumper cables can both start the engine and recharge the dead battery. Consider the automotive circuit of FIGURE P28.64. How much current is the dead battery alone able to drive through the starter motor?

검증된 단계별 안내

Identify the key components of the problem: The dead battery has an internal resistance (r_dead) and an electromotive force (emf_dead = 12 V). The starter motor has a resistance (R_motor). The goal is to calculate the current (I_dead) driven by the dead battery through the starter motor.

Apply Ohm's Law to the circuit formed by the dead battery and the starter motor. The total resistance in this circuit is the sum of the internal resistance of the dead battery (r_dead) and the resistance of the starter motor (R_motor). The total resistance is given by:

R total = r_{dead} + R_{motor}

The current driven by the dead battery can be calculated using Ohm's Law:

I dead = \frac{{emf}_{dead}}{R_{total}}

. Substitute the values of

{emf}_{dead}

r_{dead}

, and

R_{motor}

into this equation.

Simplify the equation to find the value of

I dead

. Ensure that the units are consistent (e.g., resistance in ohms, voltage in volts).

Interpret the result: The calculated current

I dead

represents the amount of current the dead battery alone can drive through the starter motor. This value will likely be small due to the increased internal resistance of the dead battery.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

15m

도움이 되었나요?

주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Ohm's Law

Ohm's Law states that the current (I) flowing through a conductor between two points is directly proportional to the voltage (V) across the two points and inversely proportional to the resistance (R) of the conductor. This relationship is expressed mathematically as I = V/R. Understanding this law is crucial for analyzing how much current a battery can provide, especially when considering the internal resistance of the battery.

Internal Resistance

Internal resistance refers to the opposition to current flow within a battery itself, caused by the chemical processes occurring during discharge. As a battery discharges, its internal resistance can increase, reducing the effective voltage available to drive current through an external circuit. This concept is essential for determining how much current a dead battery can supply to a starter motor, as higher internal resistance leads to lower current output.

Battery Capacity and State of Charge

Battery capacity is a measure of the total charge a battery can store, typically expressed in ampere-hours (Ah). The state of charge indicates how much of that capacity is currently available for use. A dead battery may have a low state of charge, affecting its ability to deliver current. Understanding these concepts helps in evaluating the performance of a battery in starting an engine and the implications of its chemical reactions on current output.

관련 실천

교과서 질문

What are the battery current I_bat and the potential difference V₁ - V₂ between points 1 and 2 when the switch in FIGURE P28.55 is (a) open and (b) closed?

170

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교과서 질문

The capacitor in an RC circuit is discharged with a time constant of 10 ms. At what time after the discharge begins are (a) the charge on the capacitor reduced to half its initial value and (b) the energy stored in the capacitor reduced to half its initial value?

150

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교과서 질문

What is the current through the 10 Ω resistor in FIGURE P28.61? Is the current from left to right or right to left?

232

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교과서 질문

How much current flows through the bottom wire in FIGURE P28.66, and in which direction?

204

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교과서 질문

A circuit you're building needs an ammeter that goes from 0 mA to a full-scale reading of 50 mA. Unfortunately, the only ammeter in the storeroom goes from 0 μA to a full-scale reading of only 500 μA. Fortunately, you've just finished a physics class, and you realize that you can make this ammeter work by putting a resistor in parallel with it, as shown in FIGURE P28.56. You've measured that the resistance of the ammeter is 50.0 Ω, not the 0 Ω of an ideal ammeter. What is the effective resistance of your ammeter?

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교과서 질문

A circuit you’re using discharges a 20 μF capacitor through an unknown resistor. After charging the capacitor, you close a switch at t = 0 s and then monitor the resistor current with an ammeter. Your data are as follows: Use an appropriate graph of the data to determine (a) the resistance and (b) the initial capacitor voltage.

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