Question

In (Figure 1) , the total resistance is 16.0k? , and the battery's emf is 25.0V . The time constant is measured to be 22.0?s . Calculate the total capacitance of the circuit. Calculate the time it takes for the voltage across the resistor to reach 17.0V after the switch is closed. Express your answer with the appropriate units.

In (Figure 1) , the total resistance is 16.0k? , and the battery's emf is 25.0V . The time constant is measured to be 22.0?s .

Part A

Calculate the total capacitance of the circuit.

Part B

Calculate the time it takes for the voltage across the resistor to reach 17.0V  after the switch is closed.

Express your answer with the appropriate units.

Answer 1

a)

Time constant

T=R*C

C=T/R =22*10^-6/16*10^3

C=1.375*10^-9 F or 1.375 nF

b)

V=Vo*e^(-t/T)

17=25*e^(-t/22*10^-6)

ln(0.68) =-t/22*10^-6

t=8.48*10^-6 s or 8.48 us

Answer 2

aTimeconstant T = RC

C = T/R
C = 22us/16000

C = 1.375 nF

b. V = V0 (1-e^-t/RC)

1-e^-t/RC = 17/25 = 0.68

e^-t/RC = 1- 0.68 = 0.32

-t/RC = ln ( 0.32) =-1.139

t = 1.139 * 22us

t = 25.05 usecs