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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 (ε), internal resistance (r), and current (I) by the following formula: V = ε - 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 (ε) and internal resistance (r) into the formula and set the terminal voltage (V) to at least 1.0 V: 1.0 ≤ 1.5 - (0.10)I
03

Solve for I

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

Calculate the maximum current

Perform the calculation: I ≤ 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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