Ch 28: Fundamentals of Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

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Knight Calc 5th Edition

Ch 28: Fundamentals of Circuits

문제 17

28장, 문제 17

The voltage across the terminals of a 9.0 V battery is 8.5 V when the battery is connected to a 20 Ω load. What is the battery's internal resistance?

검증된 단계별 안내

Identify the given values: The voltage across the terminals of the battery when connected to the load is 8.5 V, the load resistance is 20 Ω, and the battery's emf (electromotive force) is 9.0 V.

Recall the formula for the terminal voltage of a battery:

V = E - I r

, where

V

is the terminal voltage,

E

is the emf,

I

is the current, and

r

is the internal resistance.

Calculate the current

I

using Ohm's Law:

I = \(\frac{V}{R}\)

, where

V

is the terminal voltage (8.5 V) and

R

is the load resistance (20 Ω).

Substitute the values of

I

and

V

into the terminal voltage equation

V = E - I r

to solve for the internal resistance

r

. Rearrange the equation to isolate

r

r = \(\frac{E - V}{I}\)

Substitute the known values:

E = 9.0 \(\text{ V}\)

V = 8.5 \(\text{ V}\)

, and the calculated value of

I

to find the internal resistance

r

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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 V = IR. Understanding this law is crucial for analyzing circuits and calculating current, voltage, and resistance.

Internal Resistance

Internal resistance refers to the resistance within a battery that opposes the flow of current. It causes a voltage drop when the battery is supplying current, which can be calculated by the difference between the open-circuit voltage and the voltage under load. This concept is essential for understanding how real batteries perform compared to their ideal behavior.

Voltage Drop

Voltage drop is the reduction in voltage across a component in a circuit due to resistance. In the context of a battery, the voltage drop caused by internal resistance can be calculated by subtracting the load voltage from the battery's nominal voltage. This concept helps in determining how much of the battery's voltage is available for external use versus what is lost internally.