# RC and RL circuits

1. May 6, 2015

### RyanTAsher

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

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

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

3. 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 cancelled 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!

2. May 6, 2015

3. May 6, 2015

### cnh1995

For
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: May 6, 2015
4. May 6, 2015

### cnh1995

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

5. May 6, 2015

### RyanTAsher

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!

6. May 6, 2015

### RyanTAsher

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

7. May 6, 2015

### cnh1995

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