Ch 28: Fundamentals of Circuits

Knight Calc - Physics for Scientists and Engineers 5th Edition

Knight Calc5th EditionPhysics for Scientists and EngineersISBN: 9780137344796Not the one you use?Change textbook

Knight Calc 5th Edition

Ch 28: Fundamentals of Circuits

Problem 17

Chapter 28, Problem 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?

Verified step by step guidance

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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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

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.

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Related Practice

Textbook Question

Compared to an ideal battery, by what percentage does the battery's internal resistance reduce the potential difference across the 20 Ω resistor in FIGURE EX28.24?

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Textbook Question

Two of the three resistors in FIGURE EX28.23 are unknown but equal. The total resistance between points 1 and 2 is 75Ω. What is the value of R?

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Textbook Question

What is the equivalent resistance between points 1 and 2 in FIGURE EX28.27?

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Textbook Question

What is the value of resistor R in FIGURE EX28.16?

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Textbook Question

Many electric companies use time-of-day pricing in which electricity costs more during hours of high demand. Suppose electricity costs \(0.21/kWh from 10 a.m. to 6 p.m.; \)0.09/kWh at all other times. What is the annual cost of electricity for a 2.5 kW industrial pump that runs 24 hours a day?

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Textbook Question

A typical American family uses 1000 kWh of electricity a month. On average, what is the resistance of a household?

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