Calculating time constant in RC Circuit

In summary, the conversation discusses a question about finding the time constant of an RC circuit using voltage measurements on an oscilloscope. The conversation includes equations for Vc(t) and Vr(t) and mentions the time halftime formula. The attempted solution involves substituting values and solving for the time constant, but there is confusion about setting t=0 at the correct point.
  • #1

Homework Statement



You see this trace on your oscilloscope for an RC circuit. The vertical scale is 5volt/square and the horizontal scale is 50ms/square. What is the time constant of the RC circuit?

Homework Equations



Vc(t) = Vo(e^(-t/RC)
Vr(t) = -Vo * e^(-t/RC)
t halftime = Tln(2) = .69T

The Attempt at a Solution



So when the voltage is at its peak (15 V), that's Vo. and if I take that as V(t), it's V at 20 ms (approximately). Substituting this:

15 V = 15V(e^(.02/RC))
1 = e^-.02/RC
ln(1) = -.02/RC
0 = -.02/RC

Cross multiplying to solve here doesn't help me. Is there another formula I can use?
 

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  • #2
thatgirlyouknow said:

Homework Statement



You see this trace on your oscilloscope for an RC circuit. The vertical scale is 5volt/square and the horizontal scale is 50ms/square. What is the time constant of the RC circuit?

Homework Equations



Vc(t) = Vo(e^(-t/RC)
Vr(t) = -Vo * e^(-t/RC)
t halftime = Tln(2) = .69T

The Attempt at a Solution



So when the voltage is at its peak (15 V), that's Vo. and if I take that as V(t), it's V at 20 ms (approximately). Substituting this:

15 V = 15V(e^(.02/RC))
1 = e^-.02/RC
ln(1) = -.02/RC
0 = -.02/RC

Cross multiplying to solve here doesn't help me. Is there another formula I can use?

The left side of the equation is V(t) so you need to read off the value of V at 20 ms. For example, if it's 13 volts, then you will solve
[tex] 13 = 15 e^{-0.02 s/RC} [/tex]
 
  • #3
Yeah, that's what I did..I said that the V at 20 ms was 15 (the peak). Should I just pick another arbitrary time?
 
  • #4
thatgirlyouknow said:
Yeah, that's what I did..I said that the V at 20 ms was 15 (the peak). Should I just pick another arbitrary time?

But V cannot be equal to 15 volts at 0 second AND at 20 ms!

V_0 is the voltage at t=0

I think your mistake is that you did not reset t=0 at the point where the decreasing exponential starts. If you measure V_0 at the peak, you must set t=0 at that point.
 

1. What is the formula for calculating the time constant in an RC circuit?

The formula for calculating the time constant (τ) in an RC circuit is τ = R x C, where R is the resistance in ohms and C is the capacitance in farads.

2. How do I determine the resistance and capacitance values in an RC circuit?

The resistance and capacitance values can be determined by looking at the circuit diagram or by using a multimeter to measure the values of the components.

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

The time constant represents the time it takes for the voltage across the capacitor to reach approximately 63% of its maximum value in an RC circuit. It is also used to calculate the charging and discharging behavior of the capacitor in the circuit.

4. Can the time constant of an RC circuit be changed?

Yes, the time constant can be changed by altering the resistance or capacitance values in the circuit. Increasing the resistance or capacitance will result in a longer time constant, while decreasing them will result in a shorter time constant.

5. How is the time constant used in practical applications?

The time constant is used in various applications, such as in the design of filters, oscillators, and timing circuits. It is also used in electronic devices to control the charging and discharging of capacitors, as well as in the analysis of transient responses in electrical circuits.

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