For the circuit, suppose C=10µF, R1=1000Ω, R2=3000Ω, R3=4000Ω and ls=1mA. The switch closes at t=0s.1) What is the value of Vc (in volts) just prior to the switch closing? Assume that the switch had been open for a long time. 2) For the circuit above, what is the value of Vc after the switch has been closed for a long time? 3) What is the time constant of the circuit (in seconds)? Enter the answer below without units.
4) What is the value of Vc at t = 2msec (in volts).

1.) Vc = 1V

2.) Vc = 2.7V

3.) Time constant = 0.03

4.) V = 2.53V

Explanation:

1.) The value of Vc (in volts) just prior to the switch closing

The starting current = 1mA

With resistance R1 = 1000 ohms

By using ohms law

V = IR

Vc = 1 × 10^-3 × 1000

Vc = 1 volt.

2.) The value of Vc after the switch has been closed for a long time.

R2 and R3 are in parallel to each other. Both will be in series with R1

The equivalent resistance R will be

R = (R2 × R3)/R2R3 + R1

Where

R1 = 1000Ω,

R2 = 3000Ω,

R3 = 4000Ω

R = (4000×3000)/(4000+3000) + 1000

R = 12000000/7000 + 1000

R = 1714.3 + 1000

R = 2714.3 ohms

By using ohms law again

V = IR

Vc = 1 × 10^-3 × 2714.3

Vc = 2.7 volts

3.) The time constant = CR

Time constant = 10 × 10^-6 × 2714.3

Time constant = 0.027

Time constant = 0.03 approximately

4.) The value of Vc at t = 2msec (in volts). Can be calculated by using the formula

V = Vce^-t/CR

Where

Vc = 2.7v

t = 2msec

CR = 0.03

Substitute all the parameters into the formula

V = 2.7 × e^-( 2×10^-3/0.03)

V = 2.7 × e^-(0.0667)

V = 2.7 × 0.935

V = 2.53 volts

the total distance that martina travels that day is

(distance from home to mom's office) plus (distance from mom's office to school)

plus (distance from school to library) plus (distance from library to friend's house)

plus (distance from friend's house to martina's house).

(we don't know what any of these distance actually is.)