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Chapter 18: Problem 30

Find the maximum current that a fully charged D-cell can supply - if only briefly-such that its terminal voltage is at least \(1.0 \mathrm{V}\). Assume an emf of \(1.5 \mathrm{V}\) and an internal resistance of \(0.10 \Omega .\)

Short Answer

Expert verified
Answer: 5 A

Step by step solution

01

Understand the relationship between emf, internal resistance, current and terminal voltage

The terminal voltage (V) of a cell is related to emf (蔚), internal resistance (r), and current (I) by the following formula: V = 蔚 - Ir We want to find the maximum current (I) such that the terminal voltage (V) is at least 1.0 V.
02

Set up the equation

Substitute the given values of emf (蔚) and internal resistance (r) into the formula and set the terminal voltage (V) to at least 1.0 V: 1.0 鈮� 1.5 - (0.10)I
03

Solve for I

Now, we'll isolate I in the equation: I 鈮� (1.5 - 1.0)/0.10
04

Calculate the maximum current

Perform the calculation: I 鈮� 5 A The maximum current that a fully charged D-cell can supply while maintaining a terminal voltage of at least 1.0 V is 5 A.

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Most popular questions from this chapter

(a) What are the ratios of the resistances of (a) silver and (b) aluminum wire to the resistance of copper wire $\left(R_{\mathrm{Ag}} / R_{\mathrm{Cu}} \text { and } R_{\mathrm{A}} / R_{\mathrm{Ca}}\right)$ for wires of the same length and the same diameter? (c) Which material is the best conductor, for wires of equal length and diameter?
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 person can be killed if a current as small as \(50 \mathrm{mA}\) passes near the heart. An electrician is working on a humid day with hands damp from perspiration. Suppose his resistance from one hand to the other is $1 \mathrm{k} \Omega$ and he is touching two wires, one with each hand. (a) What potential difference between the two wires would cause a 50 -mA current from one hand to the other? (b) An electrician working on a "live" circuit keeps one hand behind his or her back. Why?
The starter motor in a car draws \(220.0 \mathrm{A}\) of current from the \(12.0-\mathrm{V}\) battery for \(1.20 \mathrm{s}\). (a) How much charge is pumped by the battery? (b) How much electric energy is supplied by the battery?
Consider a \(60.0-\mathrm{W}\) lightbulb and a \(100.0-\mathrm{W}\) lightbulb designed for use in a household lamp socket at \(120 \mathrm{V}\) (a) What are the resistances of these two bulbs? (b) If they are wired together in a series circuit, which bulb shines brighter (dissipates more power)? Explain. (c) If they are connected in parallel in a circuit, which bulb shines brighter? Explain.
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