Answer:
t(@95%) = 75 s
Explanation:
Given:
Time (s) 0 20 40 60 80 100 120
emf (mV) 2.5 3.8 4.5 4.8 4.9 5.0 5.0
Determine:
95 % response time t?
Solution:
To find the 95% response time t, we must calculate the 95% emf value:
emf = emf_o + 0.95*(emf_ss - emf_o)
where,
emf_o = 2.5 mV and emf_ss = 5.0 V
emf = 2.5 + 0.95*(5.0 - 2.5)
emf = 4.875 mV @ 95%
We observe that the 95% response occurs between 60 s and 80 s. To find the exact time for this response, we will use interpolation within this range:
t = m*emf + C (linear interpolation)
where,
m:slope and C: t intercept are constants
m = ( 80 - 60 ) / (4.9 - 4.8 ) = 200
C = 80 - 200*4.9 = -900 s
t(4.875) = 200*4.875 - 900
t(@95%) = 75 s
Answer: The time taken for a 95% response is t = 75 s.