You make a capacitor by cutting the 15.0-cm-diameter bottoms out of two aluminum

Question

You make a capacitor by cutting the 15.0-cm-diameter bottoms out of two aluminum pie plates, separating them by 3.35 mm , and connecting them across a 6.00 V battery.

a.What’s the capacitance of your capacitor? Express your answer to three significant figures with the appropriate units.

b. If you disconnect the battery and separate the plates to a distance of 3.50 cm without discharging them, what will be the potential difference between them?

Express your answer to three significant figures with the appropriate units.

Explanation / Answer

Assuming 15.0--cm is 15 cm, the minus sign has no meaning.
Assuming 3.50 is mm
Assuming "separate the plates to a distance of 3.50" means decreasing the spacing to 3.5 mm

Parallel plate cap
C = (A/d) in Farads
is 8.854e-12 F/m
is dielectric constant (vacuum = 1)
A and d are area of plate in m² and separation in m

A = r² = (0.085)²
C = (8.854e-12)((0.085)² / (0.00335)) = 5.99e-11 F or 59.9 pF

Q = CV = 6 x 59.9 pF = 359.4 pC

New C value is (3.35/3.5)59.9 pF = 57.33pF
Since charge is conserved, new V is
V = Q/C = 359.4 pC / 57.433pF = 6.25 volts

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