Ch 25: Current, Resistance, and EMF

Young & Freedman Calc - University Physics 15th Edition

Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo

Young & Freedman Calc 15th Edition

Ch 25: Current, Resistance, and EMF

Problema 46c

Capitolo 25, Problema 46c

A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value?

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Determine the initial power delivered to the bulb using the formula for power:

P = \frac{V^{2}}{R}

, where

V

is the total emf of the batteries and

R

is the resistance of the bulb.

Express the total emf of the batteries as

V = 1.5 + 1.5 = 3.0

V, and substitute this value along with the bulb resistance

R = 17

Ω into the power formula to calculate the initial power.

When the power decreases to half its initial value, the new power is

P = \frac{1}{2} P initial

. Use the modified power formula

P = \frac{V^{2}}{R}

, where

r

is the combined internal resistance of the batteries, to relate the new power to the total resistance.

Set up the equation for the new power:

\frac{1}{2} P initial = \frac{V^{2}}{R}

. Substitute the known values for

V

R

, and

P initial

into the equation.

Solve for the internal resistance

r

by isolating it in the equation. Rearrange the terms to express

r

in terms of the known quantities, and simplify the expression to find the combined internal resistance of the batteries.

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Concetti chiave

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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, as it helps determine how voltage, current, and resistance interact within the system.

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Resistance and Ohm's Law

Power in Electrical Circuits

The power (P) consumed by an electrical device is defined as the rate at which energy is used or converted. In a circuit, power can be calculated using the formula P = IV, where I is the current and V is the voltage. Additionally, power can also be expressed in terms of resistance as P = I²R or P = V²/R. This concept is essential for understanding how changes in resistance or current affect the power delivered to components like bulbs.

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Power in Circuits

Internal Resistance of Batteries

Internal resistance refers to the resistance within a battery that opposes the flow of current. As batteries discharge, their internal resistance can increase, affecting the voltage available to external circuits. In the context of the flashlight, the internal resistance of the batteries becomes significant when the power to the bulb decreases, as it impacts the overall voltage and current supplied to the bulb, ultimately influencing its brightness.

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Total Internal Energy

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Domanda del libro di testo

Pure silicon at room temperature contains approximately 1.0 × 10¹⁶ free electrons per cubic meter. (a) Referring to Table 25.1, calculate the mean free time t for silicon at room temperature. (b) Your answer in part (a) is much greater than the mean free time for copper given in Example 25.11. Why, then, does pure silicon have such a high resistivity compared to copper?

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Domanda del libro di testo

A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. If the batteries last for 5.0 h, what is the total energy delivered to the bulb?

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Domanda del libro di testo

A typical small flashlight contains two batteries, each having an emf of 1.5 V, connected in series with a bulb having resistance 17 Ω. If the internal resistance of the batteries is negligible, what power is delivered to the bulb?

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Domanda del libro di testo

The battery for a certain cell phone is rated at 3.70 V. According to the manufacturer, it can produce 3.15 × 10⁴ J of electrical energy, enough for 5.25 h of operation, before needing to be recharged. Find the average current that this cell phone draws when turned on.

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