You are part of a team working in a machine parts mechanic's shop. An important customer has asked your company to provide springs with a very precise force constant k. You devise the electrical circuit shown in the figure to measure the spring constant of each of the springs to be provided to the customer. The circuit consists of two identical, parallel metal plates free to move, other than being connected to identical metal springs, a switch, and a battery with terminal voltage ΔV.With the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C. When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric force between the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates that allows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. Determine an expression for the spring constant in terms of C, d, ΔV, and f. You are part of a team working in a machine parts mechanic's shop. An important customer has asked your company to provide springs with a very precise force constant k.You devise the electrical circuit shown in the figure to measure the spring constant of each of the springs to be provided to the customer. The circuit consists of two identical,parallel metal plates free to move, other than being connected to identical metal springs, a switch, and a battery with terminal voltage AV.kk+AVWith the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C. When the switch is closed, the plates become charged and attracteach other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric forcebetween the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates thatallows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. Determine an expression forthe spring constant in terms of C, d, AV, and f.kAv2k =1 -d

When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f. If the initial distance is 'd', the new distance will be 'd/f' since the value reduces by a factor of 'f' Value of the capacitance when the switch is open; C=ε0Ad Value of the capacitance when the switch is closed; C'=ε0Adf=fC The energy stored in the capacitor when the switch is open, E1=12CΔV2 The energy stored in the capacitor when the switch is closed, E2=12C'ΔV2 =12fCΔV2 The change in potential energy will be , E2-E1=12fCΔV2-12C1ΔV2 =12CΔV2f-1 The spring undergoes compression and extension. The change in length is given by d-df The potential energy of the spring will be E3=12kd-df2 At equilibrium, the potential energy of the capacitor will be equal to the potential energy of the spring. E2-E1=E312C1ΔV2f-1=12kd-df2 CΔV2f-1=kd21-1f2 CΔV2f-1=kd2f-1f2 CΔV2=kd21-ff2 k=f2CΔV2d2(f-1)

You are part of a team working in a machine parts mechanic's shop. An important customer has asked your company to provide springs with a very precise force constant k. You devise the electrical circuit shown in the figure to measure the spring constant of each of the springs to be provided to the customer. The circuit consists of two identical, parallel metal plates free to move, other than being connected to identical metal springs, a switch, and a battery with terminal voltage ΔV. With the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C. When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric force between the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates that allows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. Determine an expression for the spring constant in terms of C, d, ΔV, and f.

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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You are part of a team working in a machine parts mechanic's shop. An important customer has asked your company to provide springs with a very precise force constant k. You devise the electrical circuit shown in the figure to measure the spring constant of each of the springs to be provided to the customer. The circuit consists of two identical, parallel metal plates free to move, other than being connected to identical metal springs, a switch, and a battery with terminal voltage ΔV.

With the switch open, the plates are uncharged, are separated by a distance d, and have a capacitance C. When the switch is closed, the plates become charged and attract each other. The distance between the plates changes by a factor f, after which the plates are in equilibrium between the spring forces and the attractive electric force between the plates. To keep the plates from going into oscillations, you hold each plate with insulating gloves as the switch is closed and apply a force on the plates that allows them to move together at a slow constant speed until they are at the equilibrium separation, at which point you can release the plates. Determine an expression for the spring constant in terms of C, d, ΔV, and f.

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