- Initially the circuit of Figure 1 (above) is ?driven? by a DC source V of valu

Question

- Initially the circuit of Figure 1 (above) is ?driven? by a DC source V of value 12 volts as shown in Figure 1. Note that before switch closure the circuit has been active long enough to ensure DC steady state conditions.

- Component values:

R1 = 43 ohms C = 200 microfarads
R2 = 88 ohms V = 12 volts
R3 = 100 ohms
R4 = 33 ohms

(1) Determine the value of the voltage across the capacitance Vc immediately after
the switch closes

(2) Determine the value of the current in milliamps through resistor R4 immediately
after the switch closes

(3) Determine the final value of the current in milliamps through the resistor R4 when
the transient following the switch closure has finally died down to a steady state
DC condition.

(4) Determine the final value of the voltage across the capacitor C when the transient
following the switch closure has finally died down to a steady state DC condition

(5) Determine the voltage vc across the capacitor 5 milliseconds after the closure of
the switch

Explanation / Answer

1. R2+R3+R4=221ohm iR1+Vc=12 i*(R2+R3+R4)=Vc i=12/264 =45mA Vc=0.045*43 =1.95V 2. i*R4=2.409V 3. i*R4=2.409V 4. R2+R4=121ohm iR1+Vc=12 i*(R2+R4)=Vc i=12/164 =73mA Vc=0.073*43 =3.139V time constant=R1*C =8.6milisecs current through R1 at t=5milisecs i=0.279*e^-t/8.6 =0.156A Vc=12-i*R1 =5.292V

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