Two circular metal plates with diameter 18 cm and separated by a distance of 2mm

Question

Two circular metal plates with diameter 18 cm and separated by a distance of 2mm are connected in series with a 10 cm long cylindrical piece of material with diameter 1 mm and a 10 v battery. The space between the two circular metal plates is filled with paper which has a dielectric constant of 3.7 and the resistivity of the cylindrical piece of material is 4.2 x 10^-3m

A) what is the capacitance of the two circular metal plates with the paper?

B) what is the resistance of the cylindrical piece of material?

C) what is the time constant of the circuit?

D) when is the voltage across the capacitor at 40% of the maximum?

E) what is the maximum current in the circuit

Answers are A) C=0.42nF, B) R=535, C) 0.225 usec, D) 0.115usec and E) 0.019A

Explanation / Answer

c=keoA/d=3.7*8.85*10^-12*pie*r*r/d=0.416nF

resitance = 4.2*10^-3*0.1/pie*(0.0005)^2=535 ohm

time constant = RC = 0.416*10^-12 * 535 = 0.225usec

v = vo(1-e^(-t/RC))

for v = 40%vo e^-t/rc = 6/10 or t = ln(10/6)*RC = 0.114usec

max curent = vo/R= 10/535 = 0.019A

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