What is the time constant in an RC Circuit?

[predentalgirl1]

RC Circuits!

A capacitor in a single-loop RC circuit is charged to 63 % of its final voltage in 1.5 s. Find (a) the time constant for the circuit and (b) the percentage of the circuit's final voltage after 3.5 s.








Given that V/Vo = 63%, t = 1.5 sec , Time constant =τ
Now,
V/Vo =63%
We have, V/Vo = 1 - e –t/ τ
0.63 = 1 - e –t/ τ
e –t/ τ = 1-0.63
e t/ τ = 1/0.37
t/ τ = log 1/ 0.37
= 2.3026 x log 2.7027
1.5 /τ =2.3026 x log 2.7027
τ = 0.77?

Now to find the percentage of the circuit’s final
voltage after 3.5 sec,
V/Vo = 1- e^-3.5/.77
3.5/.77 = 2.3026 log Vo/ (Vo – V)
Or Vo/ (Vo – V) = antilog of 3.5/(.77 x 2.3026)
= 0.0106
1- (V/Vo) = 0.0106
Or V/Vo = 0.98
Therefore the percentage of the circuit’s final voltage
after 3.5 sec is 98%?

 

[Mindscrape]

Yeah, I don't see any immediate discrepancies, and you know that 5 time constants give approximately 98% of the initial voltage, which yours does. If you made a mistake is one I can't see, but you put in numbers way too soon for me to really tell what you did. Physics rule: algebra first, numbers later.

 

[Moetasim]

In summary, the time constant for the circuit is approximately 0.77 seconds and after 3.5 seconds, the capacitor will be charged to 98% of its final voltage. This information can be useful in understanding the behavior of RC circuits and designing them for specific purposes. It also highlights the importance of understanding time constants in circuit analysis.