Ch. 26 - DC Circuits

Giancoli Douglas - Physics for Scientists and Engineers 5th edition

Giancoli Douglas5th editionPhysics for Scientists and EngineersISBN: 9780137488179당신이 사용하는 게 아니라요?교과서 변경

Giancoli Douglas 5th edition

Ch. 26 - DC Circuits

문제 78

25장, 문제 78

In the circuit shown in Fig. 26–75, the 33-Ω resistor dissipates 0.80 W. What is the battery voltage?

검증된 단계별 안내

Identify the relationship between power, resistance, and current using the formula for power dissipation in a resistor:

P = I^{2} R

, where

P

is the power,

I

is the current, and

R

is the resistance.

Rearrange the formula to solve for the current

I

I = \sqrt{\frac{P}{R}}

. Substitute the given values for power (

0.80

W) and resistance (

33

Ω) into the equation.

Once the current

I

is determined, use Ohm's Law to find the voltage across the 33-Ω resistor:

V = I R

. Substitute the calculated current and the resistance value into this formula.

Analyze the circuit configuration (e.g., series or parallel) to determine how the total voltage of the battery relates to the voltage across the 33-Ω resistor. If the circuit is in series, the battery voltage is the sum of the voltage drops across all components. If in parallel, the voltage across each branch is equal to the battery voltage.

Combine the results from the previous steps to calculate the total battery voltage. Ensure that all components of the circuit are accounted for in the voltage calculation, based on the circuit's configuration.

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주요 개념

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Power Dissipation in Resistors

Power dissipation in a resistor is given by the formula P = I²R, where P is the power in watts, I is the current in amperes, and R is the resistance in ohms. This relationship shows how electrical energy is converted into heat in a resistor. Understanding this concept is crucial for determining the current flowing through the resistor when the power and resistance values are known.

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. It is mathematically expressed as V = IR. This law is fundamental in circuit analysis, allowing us to relate voltage, current, and resistance in electrical circuits.

Voltage Calculation

To find the voltage across a resistor, we can rearrange Ohm's Law to V = IR. Once we determine the current using the power dissipation formula, we can substitute it back into this equation. This process is essential for solving circuit problems where the voltage is unknown but can be derived from known power and resistance values.

관련 실천

교과서 질문

Measurements made on circuits that contain large resistances can be confusing. Consider a circuit powered by a battery ε = 15.000 V with a 10.00-MΩ resistor in series with an unknown resistor R. As shown in Fig. 26–92, a particular voltmeter reads V₁ = 366 mV when connected across the 10.00 -MΩ resistor and this meter reads V₂ = 7.317 V when connected across R. Determine the value of R. [Hint: Define R_V as the voltmeter’s internal resistance.]

711

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교과서 질문

A galvanometer has a sensitivity of 45kΩ/V and internal resistance 20.0 Ω. How could you make this into an ammeter that reads 1.0 A full scale?

809

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교과서 질문

A galvanometer has an internal resistance of 32 Ω and deflects full scale for a 48-μA current. Describe how to use this galvanometer to make a voltmeter to give a full scale deflection of 250 V.

848

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교과서 질문

A galvanometer has an internal resistance of 32 Ω and deflects full scale for a 48-μA current. Describe how to use this galvanometer to make an ammeter to read currents up to 25 A.

1288

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교과서 질문

The circuit shown in Fig. 26–89 is a primitive 4-bit digital-to-analog converter (DAC). In this circuit, to represent each digit (2ⁿ) of a binary number, a “1” has the nᵗʰ switch closed whereas zero (“0”) has the switch open. For example, 0010 is represented by closing switch n = 1, while all other switches are open. Show that the voltage V across the 1.0 - Ω resistor for the binary numbers 0001, 0010, 0100, and 1010 (which represent 1, 2, 4, 10) follows the pattern that you expect for a 4-bit DAC.

778

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교과서 질문

The performance of the starter circuit in a car can be significantly degraded by a small amount of corrosion on a battery terminal. Figure 26–88a depicts a properly functioning circuit with a battery (12.5-V emf, 0.02-Ω internal resistance) attached via corrosion-free cables to a starter motor of resistance R_s = 0.15Ω. Sometime later, corrosion between a battery terminal and a starter cable introduces an extra series resistance of only R_C = 0.10Ω into the circuit as suggested in Fig. 26–88b. Let P₀ be the power delivered to the starter in the circuit free of corrosion, and let P be the power delivered to the starter with corrosion. Determine the ratio P/P₀.

955

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