10. The current density within a section of your wire can be described as: I = (

Question

10. The current density within a section of your wire can be described as: I = (-2.7i + 5k calculatethecurrentwithinthat of your with can bedescribedas: As(40 +72 +30 )cm calculate the current within that section of the wire. 11. A charging capacitor in an RC circuit has a capacitance of 27nF and is connected to a 9V battery. The resistor in the circuit has a resistance of 0.5MO a. What is the capacitive time constant? b. After 1ms, how much charge has accumulated on the capacitor? c. How many valence electrons are there on the capacitor? d. After an additional millisecond, what is the current through the system? e. By now a total of 2ms have passed. What is the electric potential difference across the capacitor? f. What is this capacitor's half-life?

Explanation / Answer

10.

I = J.A = (-2.7i^ + 5k).(40i^ + 72 j + 30k)

I = (-2.7 x 40) + (0 x 72) + (5 x 30)

I = 42 A

11.

(A) T = RC = (0.5 x 10^6) (27 x 10^-9)

T = 0.0135 s or 13.5 ms

(B) Q = Q0 [ 1 - e^(-t/T)]

Q = (27 x 9) [1 - e^(-1/13.5)]

Q = 17.35 nC

(C) 17.35 x 10^-9 = n (1.6 x 10^-19)

n = 1.08 x 10^11 electrons

(D) I = (9 / 0.5 uA)[e^(-2/13.5)]

I = 15.52 uA  

(E) Vc = 9 - (0.5 x 15.52) = 1.24 Volt

(F) 0.5 = 1 - e^(-t/13.5)

t = 9.36 m sec

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