Two 9.0-cm-diameter metal plates 1.1 cm apart are charged to plusminus 12.5 nC.

Question

Two 9.0-cm-diameter metal plates 1.1 cm apart are charged to plusminus 12.5 nC. They are suddenly connected together by a 0.222- nun-diameter copper wire stretched taut from the center of one plate to the center of the other. What is the maximum current in the wire? Express your answer with the appropriate units. Does the current increase with time, decrease with time, or remain steady? increase with time decrease with time remain steady What is the total amount of energy dissipated in the wire? Express your answer with the appropriate units.

Explanation / Answer

Parallel plate cap
C = r(A/d) in Farads
is 8.8542e-12 F/m
r is dielectric constant (vacuum = 1)
A and d are area of plate in m² and separation in m

C = (8.85e-12)((0.045)²/(0.011)) = 5.118e-12 F

Q = CV
V = 12.5 nC/5.118e-12 pF = 2442.36 volts

current in wire is limited only by it's resistance

Resistance of a wire in
R = L/A
is resistivity of the material
L is length in meters
A is cross-sectional area in m²
A = r², r is radius of wire in m
resistivity Cu 17.2 (n-m)

R = 17.2e-9(0.011)/((0.000222)²) = 0.00122 ohm

I = E/R = 2442.36 / 0.00122 = 2.0e+6 amps. (1)

very high, but the amount of energy is very low due to the low value for C

2) it decreases with time, as the C discharges.

3) E = ½CV² Energy in a cap
E = ½(5.118p)(2442.36)² = 1.526x10^-5J

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