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Chapter 25: Problem 24

You have a \(1.0-\Omega,\) a \(2.0-\Omega,\) and a \(3.0-\Omega\) resistor. What equivalent resistances can you form using all three?

Short Answer

Expert verified
The equivalent resistance that can be formed using all three resistors are \(6.0 \Omega\) in series and approximately \(0.55 \Omega\) in parallel.

Step by step solution

01

Calculate Equivalent Resistance in Series

When the resistors are connected in series, their values are simply added together. So,Given resistors are \(1.0 \Omega\), \(2.0 \Omega\) and \(3.0 \Omega\)Equivalent resistance, \(R_{eq} = R_1 + R_2 + R_3\)\(R_{eq} = 1.0 \Omega + 2.0 \Omega + 3.0 \Omega = 6.0 \Omega.\)
02

Calculate Equivalent Resistance in Parallel

If the resistors are connected in parallel, the equivalent resistance is calculated using the formula:\(1/R_{eq} = 1/R_1 + 1/R_2 + 1/R_3\)By substituting the values given in the problem,\(1/R_{eq} = 1/1.0 \Omega + 1/2.0 \Omega + 1/3.0 \Omega\).This simplifies to,\(1/R_{eq} = 1 + 0.5 + 0.33 = 1.83 \Omega^{-1}\).Therefore, to find \(R_{eq}\), take the reciprocal of \(1.83 \Omega^{-1}\) to get \(R_{eq} = 0.55 \Omega.\)

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Most popular questions from this chapter

Two identical resistors in series dissipate equal power. How can this be, when electric charge loses energy in flowing through the first resistor?

You're writing the instruction manual for a stereo amplifier with a maximum output of 100 W. The amplifier can be modeled as an emf in series with an \(8-\Omega\) resistance. What should you specify for the loudspeaker resistance to be used with the amplifier? How much power can the amplifier deliver to a speaker with half the optimum resistance?

A \(50-\Omega\) resistor is connected across a battery, and a \(26-\mathrm{mA}\) current flows. When the resistor is replaced with a \(22-\Omega\) resistor, 43 mA flows. Find the battery's voltage and internal resistance.

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?

A new mechanic foolishly connects an ammeter with \(0.1-\Omega\) resistance directly across a \(12-\mathrm{V}\) car battery with internal resistance \(0.01 \Omega .\) What's the power dissipation in the meter? (No wonder it gets destroyed!)
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