Question in the attachment Three resistors are connected **in series** to a 95.6 V battery: \(R_1 = 3.39 \, \Omega\), \(R_2 = 9.19 \, \Omega\), and \(R_3 = 3.96 \, \Omega\). Now, as \(R_3\) heats up, its resistance increases according to:\[\frac{dR_3}{dt} = 0.366 \, \Omega/s\]Assume the resistance of the other resistors remains constant. Find \(\frac{dP}{dt}\), the rate at which the power pulled from the battery is changing in W/s, at the instant \(R_3 = 16 \, \Omega\). The sign shows whether the power is increasing or decreasing.

Answered: Three resistors are connected in series…

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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Question in the attachment

Three resistors are connected **in series** to a 95.6 V battery: \(R_1 = 3.39 \, \Omega\), \(R_2 = 9.19 \, \Omega\), and \(R_3 = 3.96 \, \Omega\). Now, as \(R_3\) heats up, its resistance increases according to:

\[
\frac{dR_3}{dt} = 0.366 \, \Omega/s
\]

Assume the resistance of the other resistors remains constant. Find \(\frac{dP}{dt}\), the rate at which the power pulled from the battery is changing in W/s, at the instant \(R_3 = 16 \, \Omega\). The sign shows whether the power is increasing or decreasing.

Expert Solution

Step 1

The total voltage of the circuit will be,

Here, I denote the current in the circuit and it will be same for all resistors because they all are connected in series and R₁, R₂, R₃denotes the resistance of the resistor one, two, three respectively.

Substituting the known values,

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