Solving Inductor Circuit Homework Problems

[kuruman]

How so? Wouldn't 30 and 60 be in series? Also 10 and 30?

Please post the redrawn circuit as I indicated in post #28 and I will explain to you what is and what is not in series and why.

 

[superslow991]

Please post the redrawn circuit as I indicated in post #28 and I will explain to you what is and what is not in series and why.

 

[kuruman]

Right. Now remember that when two resistors are in series, the current that flows through one resistor must flow through the other. That's what "in series" means. Now imagine current I starting at the battery moving to the right through the 10 Ω. It reaches the junction where the straight wire is. What happens next? Does the current go through the straight wire or does it split itself in two?

 

[superslow991]

Right. Now remember that when two resistors are in series, the current that flows through one resistor must flow through the other. That's what "in series" means. Now imagine current I starting at the battery moving to the right through the 10 Ω. It reaches the junction where the straight wire is. What happens next? Does the current go through the straight wire or does it split itself in two?

Split itself

 

[kuruman]

Split itself

Think again. If some of the current went into the right branch, then some of that current would have to go through the 60 Ω. Now Ohm's law says V = IR which means that there must be a potential difference across the 60 Ω if current flows through it. But that can't be because the potential difference across the straight wire (which the same as the potential difference across the 60 Ω) is zero. Therefore ... ?

 

[superslow991]

Think again. If some of the current went into the right branch, then some of that current would have to go through the 60 Ω. Now Ohm's law says V = IR which means that there must be a potential difference across the 60 Ω if current flows through it. But that can't be because the potential difference across the straight wire (which the same as the potential difference across the 60 Ω) is zero. Therefore ... ?

See that's where I'm lost. I understand that the potential difference would be zero but what is the straight side doing that makes the 60 ohm resistornhave the potential difference of zero? And what about the 30 ohm or 10 ohm would they have no potential difference?

 

[kuruman]

Any straight segment in a drawn circuit is by definition and convention an equipotential. This means that the potential difference between any two points on a segment connecting circuit elements is zero. For example, the potential at the positive end of the battery is the same along the wire all the way to the 10 Ω.

 

[superslow991]

Any straight segment in a drawn circuit is by definition and convention an equipotential. This means that the potential difference between any two points on a segment connecting circuit elements is zero. For example, the potential at the positive end of the battery is the same along the wire all the way to the 10 Ω.

Okay so your saying since the current would travel down where the the straight wire would be. There would be 0 potential difference and since that straight wire is parallel to the 60 ohm resistor the 60 ohm resistor will have 0 potential difference?

 

[kuruman]

Okay so your saying since the current would travel down where the the straight wire would be. There would be 0 potential difference and since that straight wire is parallel to the 60 ohm resistor the 60 ohm resistor will have 0 potential difference?

Yes. The straight wire takes all the current so the equivalent circuit is just the battery and the 10 Ω. The 30 Ω and 60 Ω are in parallel with the straight wire but they draw no current.

 

[superslow991]

Yes. The straight wire takes all the current so the equivalent circuit is just the battery and the 10 Ω. The 30 Ω and 60 Ω are in parallel with the straight wire but they draw no current.

Hmm ok thanks a lot. Very appreciative. Still kinda iffy on the 30 and 60 ohm resistors being parallel to the straight wire

 

[superslow991]

Edit*

 

[cnh1995]

Hmm ok thanks a lot. Very appreciative. Still kinda iffy on the 30 and 60 ohm resistors being parallel to the straight wire

Assume for a moment, that there is no wire. What would be the equivalent of the 30 and 60 ohm resistors?

 

[superslow991]

Assume for a moment, that there is no wire. What would be the equivalent of the 30 and 60 ohm resistors?

Hmm so if I'm reading right the 30 and 60 would be in series so are you trying to say where the 60 ohms are at it would be replaced by 90 ohms and thus it would be parallel to that straight wire to the left?

 

[cnh1995]

the 30 and 60 would be in series

No. They would be in parallel. And

it would be parallel to that straight wire to the left

 

[superslow991]

No. They would be in parallel. And

Ok could you please help me understand how the 30 and 60 ohms would be parallel cause I'm not seeing it

 

[cnh1995]

Ok could you please help me understand how the 30 and 60 ohms would be parallel cause I'm not seeing it

Replace the 15mH inductor with a wire. See the ends of the 30 ohm and 60 ohm resistance. Are they connected between the same two points?

 

[superslow991]

Replace the 15mH inductor with a wire. See the ends of the 30 ohm and 60 ohm resistance. Are they connected between the same two points?

By ends are you talking about the bottom point of the 60 ohm resistor and the edge of the 30 ohm resistor? if so then no they are not connected.

But what about when the current reaches up until the point where it can travel to the 30 ohm resistor or go down to the 60 ohm?

 

[cnh1995]

Replace the 15mH with a wire first.

By ends are you talking about the bottom point of the 60 ohm resistor and the edge of the 30 ohm resistor?

By ends, I mean the "terminals" of the resistors. For parallel connection, the four terminals ( two for each resistance) should be connected between the "same" two points.

 

[superslow991]

Replace the 15mH with a wire first.By ends, I mean the "terminals" of the resistors. For parallel connection, the four terminals ( two for each resistance) should be connected between the "same" two points.

ok so if I am reading this right. The 60 ohms terminal goes up and down. the 60 ohms terminal that's above is at the same point of the 30 ohms terminal to the left?? now the 30 ohms terminal to the left is in the same point of the 60 ohm terminal above? now the 30 ohms terminal to the right go down then connects at the same point of the 60 ohms terminal down bottom since the 15 mH inductor will just be a straight wire?

so essentially the current can go through 60 ohms or 30 ohms but not both?

 

[cnh1995]

ok so if I am reading this right. The 60 ohms terminal goes up and down. the 60 ohms terminal that's above is at the same point of the 30 ohms terminal to the left?? now the 30 ohms terminal to the left is in the same point of the 60 ohm terminal above? now the 30 ohms terminal to the right go down then connects at the same point of the 60 ohms terminal down bottom since the 15 mH inductor will just be a straight wire?

Yes.

so essentially the current can go through 60 ohms or 30 ohms but not both?

I don't know what you mean by that. If the middle wire were not there, the current would flow through both the 30 and 60 ohm reistors. But since they are in parallel with the middle wire, no current flows in either of them. Look up 'current divider'.

 

[superslow991]

Yes.

I don't know what you mean by that. If the middle wire were not there, the current would flow through both the 30 and 60 ohm reistors. But since they are in parallel with the middle wire, no current flows in either of them. Look up 'current divider'.

hmm ok so now since the 30 and 60 ohm resistors are in parallel, they would be in parallel with the 40 mH inductor that is now a straight wire. the 40 mH inductor will have 0 potential difference so since it is in parallel with the 30 and 60 ohms resistors the 60 ohm resistor will have the potential difference of 0.

So i guess somewhat in the end the circuit should just have the voltage, and 10 ohm resistor?

 

[cnh1995]

So i guess somewhat in the end the circuit should just have the voltage, and 10 ohm resistor?

Right.

 

[superslow991]

Right.

Ok thanks a lot man