Simplified circuit with R = 1k Ohm, C = 1 pF, L = 0.1 mu H, epsilon = 1 kV, ante

Question

Simplified circuit with R = 1k Ohm, C = 1 pF, L = 0.1 mu H, epsilon = 1 kV, antenna length d = 3m. The dimensions of this problem isn't very realistic. A more realistic version would require some engineering! 1. RC circuit: The system is open with an uncharged capacitor. Let's put the system in position A. Find the RC time constant T (in ns). Find the time t for which the capacitor is charged to 95% of its capacity (in ns). Find the maximum charge build-up on the capacitor q_0 (in nC) at time "infinity."

Explanation / Answer

a) Time constant = CR = 1 k ohm × 1 pF = 1 ns

b) time for 95% charge

q = 0.95 eC

q = E C (1- e^-t/RC )

0.95 E C / E C = 1-e^-t/ 1 ns

- t/ 1ns = ln (0.05 )

t = 3 ns

c) maximum charge at time (infinity ) = E C

1kV × 1pF = 1 nC

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