- #1
nickmanc86
- 10
- 0
Homework Statement
http://imgur.com/uLZdBJC27. The switch has been closed for
about 1 h. It is then opened at the time defined as t 0 s.
a. Determine the time required for the current iL to drop to
10 μA.
b. Find the voltage VL at t 10μs
c. Calculate VL at t 5tau.
Homework Equations
So I completely worked through this problem. Got Eth (20V) and Rth (1.66MΩ). Used 5H for the inductance and plugged into the formula for IL getting iL = 20V/1.66MΩ * e -t/tau where I assumed tau to be 5H/1.66MΩ= 3μs. However the answer comes out incorrect .55μs.
Looking at the solution for the book it calculates tau using only the resistance of the meter 10MΩ and gets a tau of 5μs. This of course gives the same answer as the back of the book. I do not understand why they use only the meters resistance for the tau calculation.
For part B i use the simplified release formula for VLof VL = -Vi * e-t/tau . I simply took my Vi to be Eth or 20V with my tau of 3μs and solved for VL.
However they proceed to use Vi = I*Rm where Vi = (20/1.66MΩ)*10MΩ =120V giving them VL = 120V * e-t/tau using their tau of 5μs.
I do not understand why they calculate tau using only Rmeter and then subsequently find Vi using Eth/Rth * Rmeter.
3. My Work
A)
Rth = 2MΩ||10MΩ = 1.66MΩ
Eth = 24V*10MΩ/12MΩ = 20V
Tau = L/R = 5H/1.66MΩ = 3μs
Plugged into
IL = E/R * e-t/tau -> IL = .55μs
Correct Answer = .92μs
B)
Vi = 20V
Tau = L/R = 5H/1.66MΩ = 3μs
Plugged into
VL = -Vi *e-t/tau = -0.713V
Correct answer = .81V