Take your ID number and sum the first and last digits together. Take this

value to replace the variable K in Q3 and Q4. (e.g. if your ID were

30463117, the sum would be 3 + 7 = 10 =K).

Q3.

An ideal voltage source is connected in the arrangement shown in Fig. Q3,

with three resistances and one capacitor (assumed ideal). For time t <0

all voltages and currents in the circuit are zero (including Vin(t)). For t 20

Vin(t)= K Volts.

Vin(t)

10

20 ΚΩ

(c)

40k0

Vin(t) = 0.2 d

20 ΚΩ

IB

Fig Q3

(a) Show the differential equation for Vout(t) for this circuit can

be derived as

yout de(t) + 1.5Vout(t)

4μF Vout(t)

Show each stage of the calculations

(Eq.3.1)

[5 Marks]

(b) Calculate the time constant of the circuit from the general

solution of the differential equation, using (Eq.3.1)

[5 Marks]

Determine the complete solution for Vout(t) for t20

[5 Marks]