Solving RC & RL Circuits Homework

[Destroxia]

Homework Statement

1.) If the time to achieve ½ the maximum voltage across the capacitor in an RC circuit is 0.45 s, what is the capacitance in the circuit if the resistance is 150 ohms?

2.) For an RL circuit, the voltage across the inductor drops from 4.0 V to a constant 1.5 V as a current is established. In addition the voltage across a 4.7 resistor builds to a steady 2.5 V. What is the resistance of this less than perfect inductor?

3.) If it takes 1.2 ms for the voltage across the inductor to drop from 4.0 V to 2.75V, what is the time constant for the RL circuit in question 2? Hint: What is the fraction of the total change in voltage across the inductor represented by a drop from 4.0 V to2.75 V?

4.) What is the inductance of the RL circuit in 2 and 3?

Homework Equations

q = Cε(1-e^(-t/RC) (Charging a capacitor in an RC circuit)

i = E/R(1-e^(-t/(L/R))

The Attempt at a Solution

1.) For question 1, I substituted in C(ε/2) for q

C(E/2) = CE(1-e^(-t/RC)
1/2 = e^(-t/RC)
ln(1/2) = -t/RC
C = (Rln(1/2))/-t = 2310 F

I didn't know if I could do any of these operations...

2.) For the second equation I was not sure what to do at all, I fooled around with substituting different values into the E, i, and R values, but nothing canceled the way I would need them to. I am stuck here...

3.) This one seems easy if I just knew the resistance from the second problem, I would just find a ratio of the drop of 4 to 2.75 and substitute that in with another parameter to cancel out and solve for the time constant.4.) Once again, this one is easy if I had 3, but I don't unfortunately, so I cannot calculate that inductance in the time constant.

All in all my main probelms lie with 1 and 2 then I think I could work out the rest, I just need some pointing in the right direction with my substitutions... Thank you!

 

[cnh1995]

Homework Statement

1.) If the time to achieve ½ the maximum voltage across the capacitor in an RC circuit is 0.45 s, what is the capacitance in the circuit if the resistance is 150 ohms?

2.) For an RL circuit, the voltage across the inductor drops from 4.0 V to a constant 1.5 V as a current is established. In addition the voltage across a 4.7 resistor builds to a steady 2.5 V. What is the resistance of this less than perfect inductor?

3.) If it takes 1.2 ms for the voltage across the inductor to drop from 4.0 V to 2.75V, what is the time constant for the RL circuit in question 2? Hint: What is the fraction of the total change in voltage across the inductor represented by a drop from 4.0 V to2.75 V?

4.) What is the inductance of the RL circuit in 2 and 3?

Homework Equations

q = Cε(1-e^(-t/RC) (Charging a capacitor in an RC circuit)

i = E/R(1-e^(-t/(L/R))

The Attempt at a Solution

1.) For question 1, I substituted in C(ε/2) for q

C(E/2) = CE(1-e^(-t/RC)
1/2 = e^(-t/RC)
ln(1/2) = -t/RC
C = (Rln(1/2))/-t = 2310 F

I didn't know if I could do any of these operations...

2.) For the second equation I was not sure what to do at all, I fooled around with substituting different values into the E, i, and R values, but nothing canceled the way I would need them to. I am stuck here...

3.) This one seems easy if I just knew the resistance from the second problem, I would just find a ratio of the drop of 4 to 2.75 and substitute that in with another parameter to cancel out and solve for the time constant.4.) Once again, this one is easy if I had 3, but I don't unfortunately, so I cannot calculate that inductance in the time constant.

All in all my main probelms lie with 1 and 2 then I think I could work out the rest, I just need some pointing in the right direction with my substitutions... Thank you!

Your substitutions are correct for RC circuit..But check the final answer..

 

[cnh1995]

For

Homework Statement

1.) If the time to achieve ½ the maximum voltage across the capacitor in an RC circuit is 0.45 s, what is the capacitance in the circuit if the resistance is 150 ohms?

2.) For an RL circuit, the voltage across the inductor drops from 4.0 V to a constant 1.5 V as a current is established. In addition the voltage across a 4.7 resistor builds to a steady 2.5 V. What is the resistance of this less than perfect inductor?

3.) If it takes 1.2 ms for the voltage across the inductor to drop from 4.0 V to 2.75V, what is the time constant for the RL circuit in question 2? Hint: What is the fraction of the total change in voltage across the inductor represented by a drop from 4.0 V to2.75 V?

4.) What is the inductance of the RL circuit in 2 and 3?

Homework Equations

q = Cε(1-e^(-t/RC) (Charging a capacitor in an RC circuit)

i = E/R(1-e^(-t/(L/R))

The Attempt at a Solution

1.) For question 1, I substituted in C(ε/2) for q

C(E/2) = CE(1-e^(-t/RC)
1/2 = e^(-t/RC)
ln(1/2) = -t/RC
C = (Rln(1/2))/-t = 2310 F

I didn't know if I could do any of these operations...

2.) For the second equation I was not sure what to do at all, I fooled around with substituting different values into the E, i, and R values, but nothing canceled the way I would need them to. I am stuck here...

3.) This one seems easy if I just knew the resistance from the second problem, I would just find a ratio of the drop of 4 to 2.75 and substitute that in with another parameter to cancel out and solve for the time constant.4.) Once again, this one is easy if I had 3, but I don't unfortunately, so I cannot calculate that inductance in the time constant.

All in all my main probelms lie with 1 and 2 then I think I could work out the rest, I just need some pointing in the right direction with my substitutions... Thank you!

If you read the 2nd problem carefully, the input source voltage is given to be 4V. At staedy state, it is divided as 2.5V across 4.7Ω and 1.5V across the inductor resistance..You can easily get inductor resistance from this, can't you??

 

[cnh1995]

Homework Statement

1.) If the time to achieve ½ the maximum voltage across the capacitor in an RC circuit is 0.45 s, what is the capacitance in the circuit if the resistance is 150 ohms?

2.) For an RL circuit, the voltage across the inductor drops from 4.0 V to a constant 1.5 V as a current is established. In addition the voltage across a 4.7 resistor builds to a steady 2.5 V. What is the resistance of this less than perfect inductor?

3.) If it takes 1.2 ms for the voltage across the inductor to drop from 4.0 V to 2.75V, what is the time constant for the RL circuit in question 2? Hint: What is the fraction of the total change in voltage across the inductor represented by a drop from 4.0 V to2.75 V?

4.) What is the inductance of the RL circuit in 2 and 3?

Homework Equations

q = Cε(1-e^(-t/RC) (Charging a capacitor in an RC circuit)

i = E/R(1-e^(-t/(L/R))

The Attempt at a Solution

1.) For question 1, I substituted in C(ε/2) for q

C(E/2) = CE(1-e^(-t/RC)
1/2 = e^(-t/RC)
ln(1/2) = -t/RC
C = (Rln(1/2))/-t = 2310 F

I didn't know if I could do any of these operations...

2.) For the second equation I was not sure what to do at all, I fooled around with substituting different values into the E, i, and R values, but nothing canceled the way I would need them to. I am stuck here...

3.) This one seems easy if I just knew the resistance from the second problem, I would just find a ratio of the drop of 4 to 2.75 and substitute that in with another parameter to cancel out and solve for the time constant.4.) Once again, this one is easy if I had 3, but I don't unfortunately, so I cannot calculate that inductance in the time constant.

All in all my main probelms lie with 1 and 2 then I think I could work out the rest, I just need some pointing in the right direction with my substitutions... Thank you!

As you now have the input voltage, 3rd and 4th are no longer difficult..

 

[Destroxia]

Thank you for your help, I will check my value for #1. I guess I overthought the second problem too much to the point of not seeing how simple it was... Thank you!

 

[Destroxia]

As you now have the input voltage, 3rd and 4th are no longer difficult..

Also, I rechecked my answer for 1 and got the same solution?

 

[cnh1995]

Also, I rechecked my answer for 1 and got the same solution?

If R=150 Ω, ln 0.5= -0.6931 and t=0.45 s, C should be 231 F..