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Physics / Physics with MasteringPhysics 4 / Chapter 20 / Problem 58P

Physics with MasteringPhysics | 4th Edition | ISBN: 9780321541635 | Authors: James S. Walker

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IP A parallel-plate capacitor filled with air has plates

Chapter 20, Problem 58P

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QUESTION:

Problem 58P

IP A parallel-plate capacitor filled with air has plates of are 0.0066 m2 and a separation of 0.45 mm. (a) Find the magnitude of the charge on each plate when the capacitor is connected to a 12-V battery, (b) Will your answer to part (a) increase, decrease or stay the same if the separation between the plates is increased? Explain, (c) Calculate the magnitude of the charge on the plates if the separation is 0.90 mm.

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QUESTION:

Problem 58P

IP A parallel-plate capacitor filled with air has plates of are 0.0066 m2 and a separation of 0.45 mm. (a) Find the magnitude of the charge on each plate when the capacitor is connected to a 12-V battery, (b) Will your answer to part (a) increase, decrease or stay the same if the separation between the plates is increased? Explain, (c) Calculate the magnitude of the charge on the plates if the separation is 0.90 mm.

ANSWER:

Step 1 of 2:-

Here we have to find the charge on the plate of the capacitor.

The area of the plates is,

$A=0.0066\ {m}^{2}$ .

The separation between the plates is,

$d=0.45\ mm=0.45\times{}1{0}^{-3}\ m$

The potential difference between the plates is,

$V=12\ volts$ .

We know that,

$C=\frac{Q}{V}=\frac{{\epsilon{}}_{0}A}{d}$

$\Rightarrow{}Q=\frac{{\epsilon{}}_{0}AV}{d}$ -------------(1)

$=\frac{8.85\times{}1{0}^{-12}\ F/m\times{}0.0066\ {m}^{2}\times{}12\ volts}{0.45\times{}1{0}^{-3}m}$

$=1.49\times{}1{0}^{-9}\ C$

$=1.49\times{}1{0}^{-3}\ \mu{}C$ .

So, the charge on the plates is $149\ \mu{}C$ .

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