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(a) What is the internal resistance of a voltage source if its terminal voltage drops by \(2.00 \mathrm{~V}\) when the current supplied increases by \(5.00 \mathrm{~A} ?\) (b) Can the emf of the voltage source be found with the information supplied?

Short Answer

Expert verified
(a) 0.40 ohms; (b) No, the emf cannot be found.

Step by step solution

01

Understanding the Problem

The problem asks us to find the internal resistance of the voltage source. We are given that the terminal voltage drops by 2.00 V when the current supplied increases by 5.00 A.
02

Applying Ohm's Law

We know that the change in voltage due to internal resistance (r) can be described by Ohm's Law as \( \Delta V = I \cdot r \), where \( \Delta V \) is the change in voltage and \( I \) is the change in current. Here, \( \Delta V = 2.00 \mathrm{~V} \) and \( I = 5.00 \mathrm{~A} \).
03

Solving for Internal Resistance

Rearrange the Ohm's Law equation to solve for internal resistance: \( r = \frac{\Delta V}{I} \). Substitute the given values into the equation: \( r = \frac{2.00\,\mathrm{V}}{5.00\,\mathrm{A}} \).
04

Calculating Internal Resistance

Perform the calculation: \( r = \frac{2.00}{5.00} = 0.40 \text{ ohms} \). Thus, the internal resistance is 0.40 ohms.
05

Considering the Possibility of Finding the EMF

To find the emf (electromotive force), we need the terminal voltage and the internal resistance simultaneously under a given load current, but we are only given changes in values. Therefore, with the information supplied, we cannot determine the absolute emf of the voltage source.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Ohm's Law
Ohm's Law is a fundamental principle in electrical engineering and physics that describes how voltage, current, and resistance are interrelated in an electrical circuit. It is represented by the formula \( V = I \cdot R \), where:
  • \( V \) stands for voltage, measured in volts (V).
  • \( I \) denotes current, which is the flow of electric charge, measured in amperes (A).
  • \( R \) represents resistance, measured in ohms (Ω).
This law implies that the voltage across a conductor between two points is directly proportional to the current flowing through it, given that the temperature remains constant.
In the context of internal resistance in a voltage source, Ohm's Law is applied using the equation \( \Delta V = I \cdot r \), to determine how changes in voltage relate to changes in current due to internal resistance. This relationship helps us calculate internal resistance when there's a known variation in voltage and current, allowing us to maintain efficient circuit performance.
Voltage Source
A voltage source is a two-terminal device that provides a fixed or variable potential difference (or voltage) across its terminals, driving electrical current through the circuit. It could be a battery, a power supply, or any other electronic device that maintains a constant potential.
  • Ideally, a voltage source provides consistent voltage irrespective of the load connected to it.
  • Practically, real voltage sources have internal resistance, which causes a drop in terminal voltage when current flows.
The terminal voltage of a real voltage source can thus be affected by this internal resistance. It is calculated by subtracting the voltage drop due to the internal resistance from the emf (electromotive force). Understanding the role and properties of a voltage source is crucial, especially when designing and analyzing electrical circuits to ensure that they meet the desired operational standards.
In this context, knowing the internal resistance is essential to predict how the terminal voltage might change under different load conditions, ensuring stable and reliable performance of electrical devices.
Electromotive Force (emf)
Electromotive Force (emf) is an important concept in the study of electrical circuits. Despite the name, emf is not actually a force but rather a potential difference that tends to cause electric current to flow in a circuit.
  • Emf is usually measured in volts and represents the energy supplied per charge by a source of electric power.
  • In an ideal voltage source, the terminal voltage is equal to the emf when no current flows (open circuit).
However, with real sources, internal resistance impacts the effective terminal voltage when the current is drawn. This occurs because the actual terminal voltage is reduced by the product of the internal resistance and current.
The challenge in experiments and calculations, as shown in the original problem, is determining the emf when only changes in voltage and current are provided. Without knowing either the initial terminal voltage or load conditions, the emf remains an unknown variable. Understanding emf is key to grasping how energy conversion works in a circuit and ensures the correct functioning of electrical devices by predicting and compensating for voltage drops caused by internal resistance.

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Most popular questions from this chapter

Carbon-zinc dry cells (sometimes referred to as non-alkaline cells) have an emf of \(1.54 \mathrm{~V}\), and they are produced as single cells or in various combinations to form other voltages. (a) How many \(1.54-\mathrm{V}\) cells are needed to make the common \(9-V\) battery used in many small electronic devices? (b) What is the actual emf of the approximately \(9-\mathrm{V}\) battery? (c) Discuss how internal resistance in the series connection of cells will affect the terminal voltage of this approximately \(9-\mathrm{V}\) battery.

The duration of a photographic flash is related to an \(R C\) time constant, which is \(0.100 \mu\) s for a certain camera. (a) If the resistance of the flash lamp is \(0.0400 \Omega\) during discharge, what is the size of the capacitor supplying its energy? (b) What is the time constant for charging the capacitor, if the charging resistance is \(800 \mathrm{k} \Omega ?\)

(a) Given a 48.0-V battery and \(24.0-\Omega\) and \(96.0-\Omega\) resistors, find the current and power for each when connected in series. (b) Repeat when the resistances are in parallel.

A car battery with a \(12-\mathrm{V}\) emf and an internal resistance of \(0.050 \Omega\) is being charged with a current of \(60 \mathrm{~A}\). Note that in this process the battery is being charged. (a) What is the potential difference across its terminals? (b) At what rate is thermal energy being dissipated in the battery? (c) At what rate is electric energy being converted to chemical energy? (d) What are the answers to (a) and (b) when the battery is used to supply 60 A to the starter motor?

Suppose you measure the terminal voltage of a \(1.585-\mathrm{V}\) alkaline cell having an internal resistance of \(0.100 \Omega\) by placing a \(1.00-\mathrm{k} \Omega\) voltmeter across its terminals. (See Figure.) (a) What current flows? (b) Find the terminal voltage. (c) To see how close the measured terminal voltage is to the emf, calculate their ratio.

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