A simple series circuit consists of a 130 Ohm resistor a 280

A simple series circuit consists of a 130 Ohm resistor, a 28.0 V battery, a switch, and a 2.80 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0 s. Find the electric flux at t = 0.50 ns. Find the displacement current at t = 0.50 ns.

Solution

R = 130 ohm, Voltage = 28.0 V ,  C = 2.80 pF = 2.80 * 10^-12 F

time t = 0.5 ns = 0.5 * 10^-9 s

a) FLUX  = Q / epsilon₀

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

= (2.80 * 10^-12 * 28.0 ) ( 1 - e^{(- 0.5 * 10-9 / 130 * 2.80 * 10-12 )} )

= 7.84 * 10^-11 * 0.747

Q = 5.86 * 10^-11 C

FLUX  = Q / epsilon₀

= (5.86 * 10^-11) / ( 8.85 * 10^-12 )

= 6.62 V.m

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Displacement Current

I = ( E / R ) ( e^(-t/RC) )

I = 28 / 130 * e^{(- 0.5 * 10-9 / 130 * 2.80 * 10-12 )}

I = 0.0545 A