Solve Kirchhoff's Laws for Currents and Power Dissipation in a 3-Loop Circuit

[GymGuy]

Homework Statement

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In the circuit shown below if Vs = 5V, use Kirchhoff’s Laws to determine the currents i1, i2, i3 and the source current is. Calculate the power dissipated by the resistors in this circuit. Confirm that the power dissipated by the resistors is the same as the power supplied by the power sources.

2. Homework Equations
V=IR
Kirchoffs voltage and current laws

The Attempt at a Solution

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Attempted to solve the problem using Kirchoffs voltage and current laws but can't seem to isolate a current to a value. Cant figure out where I am going wrong. This is the first question i have done involving three loops so there might be something I am not aware of?

Thanks for any help

 

[GymGuy]

In addition I am really confused by how to approach the 40 and 80 ohm resistors. They appear to be in parralel but do the nodes affect this?

 

[gneill]

It can help to clearly identify the portions of the circuit that are at the same potential (i.e. the nodes). Any components that connect to the same pair of nodes is in parallel:

Here I've used colors to distinguish the available nodes. Which components share the same node pairs?

Keep in mind that orientation and layout of components in a drawing is arbitrary, and bent, curved, or branched wiring doesn't alter the underlying topology of the circuit. What matters is what components connect to what nodes.

 

[GymGuy]

Firstly thanks for the reply.

Secondly still a little confused by what you mean? Are you saying I should redraw the diagram?

Also the red and the blue lines in your redrawn diagram signify resistors that share the same potential?

 

[gneill]

Firstly thanks for the reply.

Secondly still a little confused by what you mean? Are you saying I should redraw the diagram?

You could if it would make the circuit more clear to you; make the "geography" a closer depiction of the topology. It's up to you. If you can pick out the parallel or series arrangements from the original drawing then it's not necessary.

Also the red and the blue lines in your redrawn diagram signify resistors that share the same potential?

The colored lines just trace the wires of the circuit, using a different color to represent separate "islands" of potential. In other words, everything that's the same color belongs to a separate node. All of a given node is at the same potential throughout.

Find the components (resistors in this case) that connect to the same pairs of colors. They will be parallel connected.

 

[GymGuy]

Thanks have done that now. Does make it look more like what iam just to seeing,

Would i be right in saying that the 40 and 80 ohm resistors are not in parallel as the potential across them is different?

 

[gneill]

Thanks have done that now. Does make it look more like what iam just to seeing,

Would i be right in saying that the 40 and 80 ohm resistors are not in parallel as the potential across them is different?

Nope.

In my drawing, what are the colors of the wires connected to the ends of the 20, 40, and 80 Ohm resistors? If they are the same color pairs, then they are all in parallel.

 

[GymGuy]

Red. But the red also connects to the 10 omh resistor?

Does that mean that all of the resistors are in paralel?

 

[gneill]

Red. But the red also connects to the 10 omh resistor?

Does that mean that all of the resistors are in paralel?

What pair of colors. Every resistor has two ends. Each end is a connector. If the pair of colors is the same for two resistors then they are in parallel. Check both ends for all the resistors. Find the ones with matching pairs.