Analyzing the Circuit: Currents, Potential Differences, and Power Dissipation

[britt]

1. You are part of a team designing a go-cart. A member of the team has given you a picture of the lighting for go-cart. Your mission is to analyze the circuit. The team has not yet decided on what lights or batteries to use yet, so you need to do the analysis using variables (into which numbers will be plugged once they are decided). In the picture below five light bulbs are connected to two batteries. Treat the batteries as sources of potential difference (∆V#) and the light bulbs as resistors (R#).

A) How many different currents are in this circuit? Draw where they are.

B) How does the potential difference across R4 compare to that across R3?

C) Determine the magnitude and direction of each current (in terms of R# and ε#). Suggestion: use Kirchhoff’s rules and Ohm’s law.

D) What is the total power dissipated in the circuit? E) What answers change if light bulbs R2 and R5 are swapped?

Homework Equations

Kirchhoffs Rules

The Attempt at a Solution

B) 5 currents

C) They are equal but have opposite signs

 

[haruspex]

B) 5 currents

You mean A). How do you get 5? Are you proposing a different current through each resistor? Can you see that some must be the same?

C) They are equal but have opposite signs

You mean B). Whether they have the same or opposite signs depends which way round you measure them. Since you are not told which way to measure them, the potential differences should be considered unsigned. But out of interest, let's say we measure both from bottom to top in the diagram; what is your answer now?

 

[britt]

A) yes I assigned an I to each 5 resistors. Would the series ones be the same? R1 R2 and R5

B) I3=I4 so I34/2

 

[NascentOxygen]

B) I3=I4 so I34/2

The question asks for a comparison of potential differences.

 

[britt]

R3i3=R4i4

 

[britt]

1/R3 + 1/R4 = 1/R34 -- does this have anything to do with it?

 

[NascentOxygen]

R3i3=R4i4

Your first answer was "They are equal but have opposite signs" and haruspex questioned this. Now that you've had a chance to review your answer, would you express it any differently?

The answer will be in words.

 

[britt]

The potential difference across both are equal?

 

[haruspex]

The potential difference across both are equal?

Yes.

A) yes I assigned an I to each 5 resistors. Would the series ones be the same? R1 R2 and R5

Yes. What about the current in the wire connecting the batteries?

 

[NascentOxygen]

The potential difference across both are equal?

Correct. Since the two are connected between the same two points, the voltage across each is equal.

 

[britt]

C) don't all currents go like
_____>
| | |
^ ^ |
| | |
<___V

 

[britt]

help!

 

[haruspex]

C) don't all currents go like
_____>
| | |
^ ^ |
| | |
<___V

Yes, those are the current directions.

What about the current in the wire connecting the batteries?

Scratch that question - I see you answered it already. So yes, the currents through r1, r2, and r5 are all the same. Call it I. If the currents through R3 and R4 are I3 and I4, what two equations can you write down relating them to each other and to I?

 

[britt]

I₃₄=I₃I₄R₃R₄ / R₃₄

I₃=I₄

Not sure about how to relate them

I = I₃ + I₄ ?

 

[britt]

C) ε₂-(i₄ / r₄ + i₃ / r₃) +ε₁-ir=0

d) p= iv = (i+(i₃ + i₄))(ε₁+ε₂)

e) none would change assuming r2 and r5 have the same resistance

 

[NascentOxygen]

C) ε₂-(i₄ / r₄ + i₃ / r₃) +ε₁-ir=0

wrong

d) p= iv = (i+(i₃ + i₄))(ε₁+ε₂)

wrong

p=iv is a good start.

e) none would change assuming r2 and r5 have the same resistance

What if R2 and R5 had unequal resistance?

Give some more thought to these.