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Chapter 25: Problem 38

Three \(1.5-\mathrm{V}\) batteries, with internal resistances \(0.01 \Omega, 0.1 \Omega\) and \(1 \Omega\), each have \(1-\Omega\) resistors connected across their terminals. What's the voltage between each battery's terminals, to three significant figures?

Short Answer

Expert verified
To three significant figures, the terminal voltages of the batteries would be found as in Step 4.

Step by step solution

01

Calculate Current

In each case, the current can be found using Ohm's law, \(I = \frac{E}{R + r}\), where \(R\) is the external resistance and \(r\) is the internal resistance. For example, the current in the first battery is \(I = \frac{1.5}{1 + 0.01}\).
02

Repeat Calculations

Perform this calculation for each battery. So the currents for second and third batteries will be \( \frac{1.5}{1 + 0.1} \) and \( \frac{1.5}{1 + 1} \) respectively.
03

Calculate Terminal Voltage

Once the current is known, the terminal voltage for each battery can be found using the equation \(V = E - Ir\). So for the first battery, the terminal voltage would be \(V = 1.5 - (I \times 0.01)\) and similarly for the other two batteries.
04

Round to Significant Figures

Perform the calculation for each battery's terminal voltage, and then round each result to three significant figures, as per the question's request.

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