Solving RC & RL Circuits Homework

In summary, the first question involves finding the capacitance in an RC circuit with a resistance of 150 ohms and a time of 0.45 seconds to reach half of the maximum voltage across the capacitor. The answer is 2310 F. For the second question, the resistance of a less than perfect inductor can be found by substituting values into the equation i = E/R(1-e^(-t/(L/R)). The third question requires knowing the resistance from the second problem to find the time constant for the RL circuit. The fourth question asks for the inductance of the RL circuit in both question 2 and 3, which cannot be calculated without the resistance from question 2.
  • #1
Destroxia
204
7

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!
 
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  • #2
RyanTAsher said:

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..
 
  • #3
For
RyanTAsher said:

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??
 
Last edited:
  • #4
RyanTAsher said:

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..
 
  • #5
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!
 
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  • #6
cnh1995 said:
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?
 
  • #7
RyanTAsher said:
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..
 

1. How do I solve a RC circuit homework problem?

To solve a RC circuit homework problem, you will need to use Kirchhoff's Laws and Ohm's Law. First, analyze the circuit and determine the values of the resistors, capacitors, and voltage source. Then, use Kirchhoff's Laws to write equations for the voltage and current at each node. Finally, use Ohm's Law to solve for the unknown variables and check your solution by plugging in the values into the equations.

2. What is the difference between RC and RL circuits?

RC circuits contain a resistor and a capacitor, while RL circuits contain a resistor and an inductor. The main difference between the two is the way in which they store and release energy. Capacitors store energy in the form of an electric field, while inductors store energy in the form of a magnetic field.

3. How do I calculate the time constant in a RC circuit?

The time constant in a RC circuit is calculated by multiplying the resistance (R) by the capacitance (C). This value represents the time it takes for the capacitor to charge to about 63% of its maximum charge. The equation for time constant is τ = RC.

4. Can I use Kirchhoff's Laws to solve any RC or RL circuit?

Yes, Kirchhoff's Laws can be used to solve any circuit, including RC and RL circuits. These laws, which include Kirchhoff's Voltage Law and Kirchhoff's Current Law, are fundamental principles in circuit analysis and can be applied to any type of circuit.

5. How do I determine the voltage across a specific component in a circuit?

To determine the voltage across a specific component in a circuit, you can use Ohm's Law (V = IR) or Kirchhoff's Voltage Law. Ohm's Law is typically used for resistive components, while Kirchhoff's Voltage Law can be used for any component in a circuit. Remember to pay attention to the direction of current flow and the polarity of the voltage source when applying these equations.

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