Solving Combination Circuits for i, i1 & v

[timeforplanb]

Homework Statement

Find the equivalent resistance seen by the source and use the result to find i, i₁, and v.

Homework Equations

V=IR

for series circuits:
R_T=R₁+R₂+...+R_n
V_T=V₁+V₂+...+V_n

for parallel circuits:
I_T=I₁+I₂+...+I_n
1/R_T=(1/R₁+1/R₂+...+1/R_n)

The Attempt at a Solution

since 30Ω and 6Ω are parallel,
1/R=(1/6+1/30)=1/5
R=5

R=5Ω and 3Ω are series, so:
R_T=5+3
R_T=8Ω

i solved for the i using this:
i=V/R₁=48/3
i=16 A

in getting the total current, i did two things. is this the right thing to do?
I_T=V/R_T=48/8
I_T=9.6 A

or this?
I_T=V_T/R_T=(48+v)/8
however, i don't know how to get v there.

or are both of them wrong? help! I'm new to this that's why I'm still a little confused. thank you very much.

 

[Mindscrape]

Yeah, i is definitely wrong. Why would the full 48 volts of the source drop across the 3 ohm resistor? It wouldn't. I_T, however, should be right, what makes you say that it isn't? 48V/Rt

 

[timeforplanb]

i wasn't sure, that was all. anyways, how would i compute for the v then? and for i and i₁? can you please give me the equations? thank you.

 

[flyerpower]

You should use Kirchoff law.

48V=3I_t + 6I_1

and I_t=I_1+I_2, where I_2 is the current through the 30 ohms resistor.

You find I_2 from these equations and then use V=30(ohms)*I_2, but i don't understand what + V - means.. anyway the absolute value should be right, I'm not sure if it's negative or positive, it depends on what that sign means (+ V -)

 

[gneill]

Note the polarity of the battery in the circuit. The + terminal is on the bottom. Since it's the only source in the circuit you can be sure that it will drive current out of its + terminal and into the circuit. That means that the actual current flows should looks as in the attached figure where they're indicated in red.

Note that these "actual" currents run counter to the currents originally labelled on the circuit diagram. You should assume that those labelled directions (as well as the indicated polarity for v across the 50 Ohm resistor) are the ones that are to be used for purposes of reporting your answers. That is, in this case the values that you will assign to i, i1, and v will be negative.

 

[timeforplanb]

thank you flyerpower!
gneill - i'll keep that in mind. thanks, too :D