Question

In (Figure 1), the total resistance is 15.0 kΩ , and the battery's emf is 31.0 V . The time constant is measured to be 26.0 μs .

Part A

Calculate the total capacitance of the circuit.

Express your answer with the appropriate units.

C =

SubmitRequest Answer

Part B

Calculate the time it takes for the voltage across the resistor to reach 15.0 V after the switch is closed.

Express your answer to three significant figures and include the appropriate units.

t =

Answer 1

Given

RC circuit with

R= 15 k ohm ,

V = 31.0 V

Time constat T = 26*10^-6 s

PartA

we know that in RC circuit the time constant or Characteristic time is T = R*C

so T = R*C

C = T/R

C = (26*10^-6)/ (15*10^3) F

C = 1.733*10^-9 F

C = 1.733 nF

Part B

for voltage the expression is  

V(t) = V0*e^(-t/T))

where V0 is maximum value V = 31 V

15 = 31 e^(-t/(26*10^-6)) s

t = 1.887436*10^-5 s

so the time taken to recha the voltage across the resistor from 31 to 15 V is 1.887436*10^-5 s