Parallel and Series circuits w/ multiple batteries

[Gothy]

Hello, this is my first time posting on this forum and I have seeked help on this forum before on previous assignments for my physics class.

There are four problems that I do not understand clearly or do not understand how the image is portrayed in a blueprint format

Problem 1

Homework Statement

http://img291.imageshack.us/img291/4382/problem39.jpg
Find i

Homework Equations

Kirchhoff's rules

The Attempt at a Solution

I can find 2 loops with Kirchhoff's rules, but it is not enough to find i.
6 - 3.5i₂ - 2.2i = 0; 6 - 3.5i₁ - 2.2i = 0; I understand I need to find a loop without i so I can eliminate i₂ or i₁ from one of the equations, but I do not understand the concept of two batteries facing each other.
I tried using
i₂=i₃+i or i = i₂ - i₃ and i just comes out to 0
Problem 2

Homework Statement

http://img175.imageshack.us/i/problem30.jpg/"

If the emf of the battery is 15 V, and each resistance is 2, what is the power consumed by bulb B?

Bulb D is then removed from its socket.How does the brightness of bulb A change?

How does the brightness of bulb B change when bulb D is removed from its socket?

Homework Equations

not sure?

The Attempt at a Solution

The picture itself is confusing to me. I do not get how to put the light bulb picture into a blueprint format. Any information on simplifying this image would be amazing.

Problem 3

Homework Statement

http://img687.imageshack.us/i/problem25.jpg/"
Find the equivalent resistance R between points A and B of the resistor network.

Homework Equations

series circuit resistance = R₁+R₂+R₃...
Parallel circuit resistance= [(1/R₁) + (1/R₂) + (1/R₃)]^-1

The Attempt at a Solution

(1/(41+21+26)+1/33)^-1= 264/11
[(1/(21+ 264/11)) + 1/36]^-1 = 1980/59 = 33.55932203

Solved Final answer = 20


Problem 4

Homework Statement

http://img85.imageshack.us/i/problem22.jpg/"

R = [(675-486)/5.8] - .36 - .16 - 1.15= 30.9162069

Find the potential difference V_xy = V_x − V_y between points X and Y

How much energy UE is dissipated by the 1.15 in 55 s ?

Homework Equations

V_xy = V_x − V_y
P=IV
V=IR

The Attempt at a Solution

Once again the negative sides facing each other completely throw me off and I have no Idea what to do.

 

[vela]

Problem 1

Homework Statement

http://img291.imageshack.us/img291/4382/problem39.jpg
Find i

Homework Equations

Kirchhoff's rules

The Attempt at a Solution

I can find 2 loops with Kirchhoff's rules, but it is not enough to find i.
6 - 3.5i₂ - 2.2i = 0; 6 - 3.5i₁ - 2.2i = 0; I understand I need to find a loop without i so I can eliminate i₂ or i₁ from one of the equations, but I do not understand the concept of two batteries facing each other.

There's nothing particularly special about having the two batteries in the circuit. Your equations are fine.

You can get the third equation using Kirchoff's current law to relate i, i1, and i2. In this particular case, because of the symmetry of the circuit, you might see that i1 and i2 have to be equal.

 

[vela]

Problem 3

Homework Statement

http://img687.imageshack.us/i/problem25.jpg/"
Find the equivalent resistance R between points A and B of the resistor network.

Homework Equations

series circuit resistance = R₁+R₂+R₃...
Parallel circuit resistance= [(1/R₁) + (1/R₂) + (1/R₃)]^-1

The Attempt at a Solution

(1/(41+21+26)+1/33)^-1= 264/11
[(1/(21+ 264/11)) + 1/36]^-1 = 1980/59 = 33.55932203

Your method is fine. You just made a mistake somewhere churning out the final answer.

 

[Gothy]

Problem 1 and 3 are done, can anyone help with the last two?

 

[vela]

Problem 2

Homework Statement

http://img175.imageshack.us/i/problem30.jpg/"

If the emf of the battery is 15 V, and each resistance is 2, what is the power consumed by bulb B?

Bulb D is then removed from its socket.How does the brightness of bulb A change?

How does the brightness of bulb B change when bulb D is removed from its socket?

Homework Equations

not sure?

The Attempt at a Solution

The picture itself is confusing to me. I do not get how to put the light bulb picture into a blueprint format. Any information on simplifying this image would be amazing.

There are only two loops in the circuit. Go around each one, placing and connecting the resistors as appropriate.

 

[vela]

Problem 4

Homework Statement

http://img85.imageshack.us/i/problem22.jpg/"

R = [(675-486)/5.8] - .36 - .16 - 1.15= 30.9162069

Find the potential difference V_xy = V_x − V_y between points X and Y

How much energy UE is dissipated by the 1.15 in 55 s ?

Homework Equations

V_xy = V_x − V_y
P=IV
V=IR

The Attempt at a Solution

Once again the negative sides facing each other completely throw me off and I have no Idea what to do.

Like I said for problem 1, you don't have to do anything differently when analyzing a circuit with two voltage sources. You seem to have a decent grasp of the material. Just get past that mental block and just do what you've been doing.

 

[Gothy]

I have tried drawing it and I only need to figure out how much Power is consumed by the B bulb. My design is an attachment below

(each resistor A,B,C, and D are 2 Ohms)
And I keep getting P_B = 18 which is not correct
Did I set up my circuit right?

 

[Gothy]

Like I said for problem 1, you don't have to do anything differently when analyzing a circuit with two voltage sources. You seem to have a decent grasp of the material. Just get past that mental block and just do what you've been doing.

I found the Vx= 189 and I subtracted [5.8(1.15+.36)] because of voltage drops and I got 180.242.

 

[vela]

I have tried drawing it and I only need to figure out how much Power is consumed by the B bulb. My design is an attachment below

(each resistor A,B,C, and D are 2 Ohms)
And I keep getting P_B = 18 which is not correct
Did I set up my circuit right?

Yes, you drew the circuit correctly. Show us how you calculated P_B.

 

[vela]

I found the Vx= 189

This doesn't make sense. It's 189 volts relative to what?

I assume you got the 189 V by subtracting 486 V from 675 V. That 189 V would be the voltage difference between the point to the left of the 675-V battery and the point to the right of the 486-V battery.

and I subtracted [5.8(1.15+.36)] because of voltage drops and I got 180.242.

Try applying Kirchoff's voltage law going around the loop starting from point Y, jumping straight up to point X, and then going to the left through the 675-V battery and the two resistors.

 

[Gothy]

Yes, you drew the circuit correctly. Show us how you calculated P_B.

I first calculated the equivelent resistance:
(1/(2+2) + 1/2)^-1 = 4/3
4/3 + 2 = 10/3
R_eq= 10/3

With the total resistance I found the whole circuit's current:
V=IR
I=V/R
I= 15 * 3/10= 4.5

next, I found the allocated towards the parallel circuit so I subtracted the voltage dropped from A immediately.
V_A=IR
V_A= 4.5*2 = 9

So, 6 volts allocated towards B,C, and D.
P_B=IV
P_B=V²/R_B
P_B= 36/2
P_B=18

 

[Gothy]

This doesn't make sense. It's 189 volts relative to what?

I assume you got the 189 V by subtracting 486 V from 675 V. That 189 V would be the voltage difference between the point to the left of the 675-V battery and the point to the right of the 486-V battery.

Try applying Kirchoff's voltage law going around the loop starting from point Y, jumping straight up to point X, and then going to the left through the 675-V battery and the two resistors.

So what you're saying is to do 675 - 5.8*.36 - 5.8*1.15 = the potential difference? How is there a loop for the electricity to flow?
It is right but I do not understand how it works.

 

[vela]

I first calculated the equivelent resistance:
(1/(2+2) + 1/2)^-1 = 4/3
4/3 + 2 = 10/3
R_eq= 10/3

With the total resistance I found the whole circuit's current:
V=IR
I=V/R
I= 15 * 3/10= 4.5

next, I found the allocated towards the parallel circuit so I subtracted the voltage dropped from A immediately.
V_A=IR
V_A= 4.5*2 = 9

Perfect up to here.

So, 6 volts allocated towards B,C, and D.
P_B=IV
P_B=V²/R_B
P_B= 36/2
P_B=18

6 volts is the drop the series combination of B and C, not across B and C individually. Your answer would be correct for the power dissipated by D since the entire 6-volt drop appears across that resistor, but with B and C, the voltage drops across the individual resistors add up to 6 volts.

 

[Gothy]

Perfect up to here.

6 volts is the drop the series combination of B and C, not across B and C individually. Your answer would be correct for the power dissipated by D since the entire 6-volt drop appears across that resistor, but with B and C, the voltage drops across the individual resistors add up to 6 volts.

This makes PERFECT sense! Thank you so much! I was thinking the same thing but I got confused and I forgot the square the V so instead of 4.5 I ended up with 9.

 

[vela]

So what you're saying is to do 675 - 5.8*.36 - 5.8*1.15 = the potential difference? How is there a loop for the electricity to flow?
It is right but I do not understand how it works.

Yes, that's the correct equation.

You get used to going around the actual loops in a circuit because that's how you usually get your equations, but KVL actually applies to any loop. As long as you end up in the same place as you started, the voltage differences around the loop must sum to zero.