A RC circuit consists of a 4 F capacitor a 1.5 M resistor, and a 12 volt power s

Question

A RC circuit consists of a 4 F capacitor a 1.5 M resistor, and a 12 volt power supply. When the circuit is energized with direct current What is the time constant for this circuit? What is the steady state value of the current? What is the steady state value of the potential across the capacitor? What is the potential across the capacitor at t = 5.55 seconds? What is the current through the circuit at t = 5.55 seconds. What is the current through the circuit after 1 time constant has elapsed? What is the potential across the capacitor after 1 time constant has elapsed? Plot current versus time and voltage versus time for a charging capacitor. The longer time the current decreases

Explanation / Answer

(1)

Time cosntant T = R*C = 1.5*10^6*4*10^-6 = 6 s

(b)

I = Imax*e^(-t/RC)

For steady state current t ->

I = 0

(c)

Steady state voltage,

V = 12 volts

(d)

V(5.55) = Vmax *(1-e^(-t/T))

= 12*[1-e^(-5.55/6)]

= 7.24 volts

(e)

I = Imax *e^(-5.55/6)

= [12/1.5*10^6]*e^(-5.55/6)

=3.17 810^-6 ohm

(f)

I = Imax *e^(1)

= Vmax/R*e

= [12/1.5*10^6]*e^-1

=2.94*10^-5 A

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