Thank you Steve! I got the answer. In the problem, the anode voltage must be greater than the cathode voltage for the diode to conduct! So, 2t-1 > 10 . When I solve for t, I get 5.5s .
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This is one possible solution (and very probably the one that was intended by the author of the assignment).
There is, however an infinity of possible solutions as the equation defining the bahaviour of VS is ill defined.
Where it states
Vs = 2t-1 volts
it is not defined in which units t shall be measured. Of course, as subsequently the value of "time (in seconds)" is to be given, one can assume that this is the unit to be used for t.
The correct equation should then read
Vs = 2 V/s*t - 1 V
which allows for a clearly defined solution with t = 5.5 s.
The original statement
Vs = 2t-1 volts
could also be solved with t = 5.5 h, t = 5.5 ms etc. as units are missing.
This is not your fault, it's the author's fault.
It is always a good idea to include units into your equations and keep them throughout the calculation. It wil help you identify mistakes e.g. when units don't match or exponents mismatch.
