You make a capacitor by cutting the 12.5-cm-diameter bottoms out of two aluminum
ID: 581921 • Letter: Y
Question
You make a capacitor by cutting the 12.5-cm-diameter bottoms out of two aluminum pie plates, separating them by 3.60 mm , and connecting them across a 6.00 V battery.
1) What’s the capacitance of your capacitor?
Express your answer to three significant figures with the appropriate units.
2) 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 12.5--cm is 12.5 cm, the minus sign has no meaning.
Assuming 3.60 is mm
Assuming "separate the plates to a distance of 3.60" means decreasing the spacing to 3.6 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 = (0.0625)²
C = (8.854e-12)((0.0625)² / (0.00360)) = 0.301e-11 F or 3.01 pF
Q = CV = 6 x 3.01 pF = 18.06 pC
New C value is (3.60/3.5)3.01 pF = 3.096 pF
Since charge is conserved, new V is
V = Q/C = 18.06 pC / 3.096 pF = 5.83 volts
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