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Chapter 18: Problem 36

Suppose a collection of five batteries is connected as shown. (a) What is the equivalent emf of the collection? Treat them as ideal sources of emf. (b) What is the current through the resistor if its value is \(3.2 \Omega ?\)

Short Answer

Expert verified
Question: Given an arrangement of five ideal batteries with emf values \(E_1\), \(E_2\), \(E_3\), \(E_4\), and \(E_5\), find the equivalent emf and the current flowing through a \(3.2 \Omega\) resistor connected to the arrangement. Solution: (a) The equivalent emf is ______. (b) The current through the resistor is ______.

Step by step solution

01

Analyze the Battery Configuration

First, we need to observe the given configuration of the batteries and note down their emf values and arrangement (whether they are connected in series or parallel). The arrangement might look like this: - Battery 1, emf: \(E_1\) - Battery 2, emf: \(E_2\) - Battery 3, emf: \(E_3\) - Battery 4, emf: \(E_4\) - Battery 5, emf: \(E_5\)
02

Calculate the Equivalent EMF

The formula for equivalent emf in series is the algebraic sum of the individual emf values, and in parallel, it is the ratio of the sum of the product of the emf values and their internal resistances to the sum of the internal resistances. As we are asked to treat them as ideal sources of emf, we can consider their internal resistance to be zero. The problem can be solved more easily by treating each part of the combination separately. Based on the specific arrangement given, determine the equivalent emf values for the individual parts and then find the total equivalent emf of the collection.
03

Apply Ohm's Law to Find the Current Through the Resistor

Ohm's law states that \(I = \frac{E_{eq}}{R}\), where \(I\) is the current through the resistor, \(E_{eq}\) is the equivalent emf, and \(R\) is the resistance. Use the equivalent emf found in step 2 and the given resistance value (\(3.2 \Omega\)) to calculate the current through the resistor.
04

Write the Final Answer

After performing the calculations in steps 2 and 3, report the equivalent emf of the battery collection and the current flowing through the resistor. The final answer will be in the format: (a) The equivalent emf is ______. (b) The current through the resistor is ______.

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Most popular questions from this chapter

A 6.0 -pF capacitor is needed to construct a circuit. The only capacitors available are rated as \(9.0 \mathrm{pF} .\) How can a combination of three 9.0 -pF capacitors be assembled so that the equivalent capacitance of the combination is \(6.0 \mathrm{pF} ?\)
A gold wire and an aluminum wire have the same dimensions and carry the same current. The electron density (in electrons/cm \(^{3}\) ) in aluminum is three times larger than the density in gold. How do the drift speeds of the electrons in the two wires, \(v_{\mathrm{Au}}\) and \(v_{\mathrm{Al}},\) compare?
In the physics laboratory, Oscar measured the resistance between his hands to be \(2.0 \mathrm{k} \Omega .\) Being curious by nature, he then took hold of two conducting wires that were connected to the terminals of an emf with a terminal voltage of \(100.0 \mathrm{V} .\) (a) What current passes through Oscar? (b) If one of the conducting wires is grounded and the other has an alternate path to ground through a \(15-\Omega\) resistor (so that Oscar and the resistor are in parallel), how much current would pass through Oscar if the maximum current that can be drawn from the emf is \(1.00 \mathrm{A} ?\)
(a) In a charging \(R C\) circuit, how many time constants have elapsed when the capacitor has \(99.0 \%\) of its final charge? (b) How many time constants have elapsed when the capacitor has \(99.90 \%\) of its final charge? (c) How many time constants have elapsed when the current has \(1.0 \%\) of its initial value?
An ammeter with a full scale deflection for \(I=10.0 \mathrm{A}\) has an internal resistance of \(24 \Omega .\) We need to use this ammeter to measure currents up to 12.0 A. The lab instructor advises that we get a resistor and use it to protect the ammeter. (a) What size resistor do we need and how should it be connected to the ammeter, in series or in parallel? (b) How do we interpret the ammeter readings?
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