Problem 5: 20 k2 10 kl www www Find the output voltage v, when the source v, = 6u(1) V and v,(0) =1 V. Recall that u(1) represents the unit step 40 2 3 µF function. ww
The source voltage is function of unit step function which means the source voltage is zero when time is less than zero.
The voltage across the capacitor at any time for the given circuit is given by:
Where,
The steady state voltage across the capacitor is “VSS”,
The initial voltage across the capacitor is “VO (0)” which is 1 V,
The equivalent resistance across the capacitor terminal is “Req”,
The capacitance of capacitor is “C”.
In steady state condition, the capacitor will act as open circuit and no current will flow from the 10 kΩ resistor and the voltage across the capacitor is equal to voltage across the 40 Ω resistor. To calculate the voltage across the 40 Ω resistor, apply voltage division rule in loop containing voltage source, 20 kΩ resistor and 40 Ω resistor:
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