Chemists (and Astronomers!) like to express lengths in Angstrom units where 1 An

Question

Chemists (and Astronomers!) like to express lengths in Angstrom units where 1 Angstrom = 10^-10 m, roughly the length of a chemical bond. What is the repulsive energy of two protons that are 1 Angstrom unit apart? State your answer in both Joules and Electron Volts. The resistivity of carbon is 3.5 times 10^-5 Ohm m. Remembering that R=rho L/A, how long a piece of carbon, 1 mm in radius would be needed for a 4000 Ohm resistor. What would the electric field be inside the resistor if the two ends were kept at a 5 volt difference in potential? A 2000 Ohm resistor and a 125 mu F capacitor are connected in series and the combination placed across the terminals of a 100 Volt battery. What is the current through the resistor a time 0? What will the current be at long times? What is the charge stored in the capacitor at time 0? What will the charge be at long times?

Explanation / Answer

B)   Repulsive energy = U = e^2/R = (1.6*10^-19)^2/10^-10 = 2.56*10^-28 J = 1.6*10^-9 eV

C)    = 3.5*10^-5 ohm-m

      A = pi*r^2 = pi*10^-6 = 3.14*10^-6 m^2

      R = 4000 ohm

      Now   L = RA/ = (4000*3.14*10^-6)/3.5*10^-5 = 358.86 m

       Electric field = E = V/L = 5/358.86 = 0.01393 N/C

D) a) Current through resistor at t = 0 ===> I = V/R = 100/2000 = 0.05 A

b) Current after long time = I = 0.05 A

c) Charge stored in capacitor at time 0 ===> Q = 0

d) Charge after long time = Q = CV = 125*10^-6*100 = 0.0125 C

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