What is the inductance needed for a maximum potential difference?

[Pepsi24chevy]

I have a problem that goes as followed: http://www.webassign.net/pse/p32-19.gif
Consider the circuit in Figure P32.17, taking = 6 V, L = 4.00 mH, and R = 6.00

(a) What is the inductive time constant of the circuit?
I found this to be .6667 ms
(b) Calculate the current in the circuit 250 µs after the switch is closed.
AI found this to be .312A

NOw i don't know what to do with part C and D.
(c) What is the value of the final steady-state current?


(d) How long does it take the current to reach 80% of its maximum value?
ms

 

[hotvette]

I presume you derived an equation relating current and time. Hint: steady state current is current at:

$$t = \infty$$

For the other, you want t such that

$$I = 0.8 \ I_{ss}$$

 

[Corneo]

As $t \to \infty$, the inductor is shorted out and becomes simply a wire. Meaning, as $t \to \infty$, your circuit will simply have a source, switch, and a resistor.

 

[Pepsi24chevy]

ok i got c which was 1. I still don't understand the last part.

 

[hotvette]

I believe you have an equation expressing I as a function of t:

(1) $I = f(t)$

You also know the steady state current, $I_{ss}$. What you want to do is solve (1) for $t$ when $I = 0.8 \ I{ss}$.

 

[Pepsi24chevy]

ok, thanks i got it

 

[BobG]

You understand how the time constant works, right?

Your current is equal to:

$$i(t)=i_f * e^{\frac{-t}{\tau}$$

You've figured out your final current in part c. You figured out your time constant in part a. You current, i(t), is .8 times the final current. The only unknown variable is t. Best way to start is to take the natural log of both sides. That leaves a pretty easy equation to solve.

 

[Pepsi24chevy]

3 physics problems concerninginductance and rlc circuit

1. "The resistance of a superconductor." In an experiment carried out by S. C. Collins between 1955 and 1958, a current was maintained in a superconducting lead ring for 2.50 yr with no observed loss. If the inductance of the ring was 3.14 10-8 H and the sensitivity of the experiment was 1 part in 109, what was the maximum resistance of the ring? (Suggestion: Treat this problem as a decaying current in an RL circuit and recall that e -x 1 - x for small x.)

So i have(R/L)t=10e-9 So i plug in and i get 3.98e-23 in which the program i am using says my answer is off by a magnitude of 10. I have recalculated it a few times and i get the same answer.


2.http://www.webassign.net/pse/p31-09.gif
On a printed circuit board, a relatively long straight conductor and a conducting rectangular loop lie in the same plane, as shown in Figure P31.9. Taking h = 0.600 mm, w = 1.30 mm, and L = 2.30 mm, find their mutual inductance

With this problem, the long straight conductor and the loop aren't the same shape, so i don't know how to go about solving this. I know the forumla for mutual inductance for two wires, but that is about it.

3.http://www.webassign.net/pse/p32-50.gif
[PSE6 32.P.048.] In the circuit of Figure P32.48, the battery emf is 75 V, the resistance R is 220 , and the capacitance C is 0.500 µF. The switch S is closed for a long time, and no voltage is measured across the capacitor. After the switch is opened, the potential difference across the capacitor reaches a maximum value of 150 V. What is the value of the inductance L?

FOr this problem, i don't see how to find L using angular frequency= (1/sqrt(LC)) with the variables and info i am givin. That is the only equation i can find in my book to use.