Answered: Inductive battery chargers, which allow…

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

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Inductive battery chargers, which allow transfer of electrical power without the need for exposed electrical contacts, are commonly used in appliances that need to be safely immersed in water, such as electric toothbrushes. Consider the following simple model for the power transfer in an inductive charger (see the figure).(Figure 1) Within the charger's plastic base, a primary coil of diameter ddd with nPnP turns per unit length is connected to a home's ac wall outlet so that a current I=I0sin(2πft)I=I0sin(2πft) flows within it. When the toothbrush is seated on the base, an NNN-turn secondary coil inside the toothbrush has a diameter only slightly greater than ddd and is centered on the primary.

Find an expression for the emf induced in the secondary coil. [This induced emf recharges the battery.]

Express your answer in terms of the variables ddd, nPnPn_P, I0I0I_0, fff, ttt, NNN, and appropriate constants.

Problem 29.24
Constants | P
Inductive battery chargers, which allow transfer of
electrical power without the need for exposed electrical
contacts, are commonly used in appliances that need to
be safely immersed in water, such as electric
toothbrushes. Consider the following simple model for
the power transfer in an inductive charger (see the
figure). (Figure 1) Within the charger's plastic base, a
primary coil of diameter d with np turns per unit length
is connected to a home's ac wall outlet so that a current
I = Iosin(27 ft) flows within it. When the toothbrush
is seated on the base, an N-turn secondary coil inside
the toothbrush has a diameter only slightly greater than
d and is centered on the primary.
Part A
Find an expression for the emf induced in the secondary coil. [This induced emf recharges the battery.]
Express your answer in terms of the variables d, np, Io, f, t, N, and appropriate constants.
Hνα ΑΣφ
e2 =
Figure
1 of 1
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Primary coil
(in charger base)
Secondary coil
(in toothbrush)
FI=Lsin(2m)

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