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Chapter 25: Problem 68

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.

Short Answer

Expert verified
The battery's voltage is around \(1.45 \, V\) and the internal resistance is about \( 5 \, \Omega\).

Step by step solution

01

Formulate First Scenario

Start by representing the first scenario using Ohm's law for the circuit when a 50-Ω resistor is placed. In this case, the current, I1 is 26 mA and R1 is 50 Ω. The battery's Emf (E) and the internal resistance (r) formulates the equation E = I1*(R1 + r).
02

Formulate Second Scenario

Next, formulate the equation for the second scenario with a 22-Ω resistor and the current, I2 as 43 mA and R2 = 22 Ω. We get E = I2 * (R2 + r).
03

Solve Equations

Since we have 2 equations with 2 unknowns (E and r), we can now solve them simultaneously. Start by equating the two equations E = I1 * (R1 + r) and E = I2 * (R2 + r), this would give the value of internal resistance r. We then substitute the value of r into one of the equations to get E.

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Most popular questions from this chapter

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?

Show that a battery delivers the most power when the load resistance across its terminals is equal to its internal resistance. (This is not the way to treat a battery, but it's the basis for load matching in amplifiers; see Problem \(65 .\) )

A student who's confused about voltage and current hooks a nearly ideal ammeter across a car battery. What happens?

An uncharged \(10-\mu \mathrm{F}\) capacitor and a \(470-\mathrm{k} \Omega\) resistor are in series, and \(250 \mathrm{V}\) is applied across the combination. How long does it take the capacitor voltage to reach \(200 \mathrm{V} ?\)

Sketch a circuit diagram for a circuit that includes a resistor \(R_{\square}\) connected to the positive terminal of a battery, a pair of paralle resistors \(R_{2}\) and \(R_{3}\) connected to the lower-voltage end of \(R_{1}\) and then returned to the battery's negative terminal, and a capacitor across \(R_{2}\)
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