RC Circuits and time constants

In summary, the conversation discusses finding the time constant and percentage of final voltage in an RC circuit. The time constant is found to be 0.77 seconds and the final voltage after 3.5 seconds is approximately 98% of the initial voltage. The conversation also mentions the importance of using algebra before plugging in numbers in physics problems.
  • #1
predentalgirl1
67
1
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%?
 
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  • #2
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.
 
  • #3


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.
 
1.

What is an RC circuit?

An RC circuit is an electrical circuit that is composed of a resistor (R) and a capacitor (C) connected in series. These components are used to control the flow of electric current in a circuit and can be found in a variety of electronic devices.

2.

What is the purpose of a time constant in an RC circuit?

The time constant, represented by the symbol τ (tau), is a measure of how quickly a capacitor charges or discharges in an RC circuit. It is used to determine the rate at which the voltage across the capacitor or the current through the circuit changes over time.

3.

How do I calculate the time constant of an RC circuit?

The time constant of an RC circuit can be calculated using the formula τ = R x C, where R is the value of the resistor in ohms and C is the value of the capacitor in farads. The resulting time constant is measured in seconds.

4.

What is the significance of the time constant in an RC circuit?

The time constant is an important parameter in an RC circuit as it determines the rate at which the capacitor charges or discharges. It is also used to calculate the time it takes for the capacitor to reach a certain percentage of its maximum charge or discharge, known as the charging or discharging time.

5.

How does increasing or decreasing the values of R and C affect the time constant in an RC circuit?

Increasing the values of R and C will result in a longer time constant, meaning that the capacitor will take longer to charge or discharge. Conversely, decreasing the values of R and C will result in a shorter time constant and a faster charging or discharging time for the capacitor.

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