# Kirchoff's Law for 3 loop circuit with multiple voltage supplies

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#### ZeroSumPlayer

##### New Member
Hi,

I am working on the below circuit to find; the power dissipated by RL (8Ω resistor), voltage drop across RL and current supplied by the 10 volt battery (V1).

So far I have used Kirchoff's law to the best of my ability to get 3 loop equations but 4 unknowns, I am thrown off by the variable voltage supply V3 = 3Is

In my workings I have used I1=Is for simplicity.

Loop 1

0 =10 - 6I1 - 20I2

Loop 2

0 = 35 I1 - 11 I1 - 6 I3 - 5V

Loop 3

0= 4 I1 - 14 I3 - 18 I4 (V3 = 4I1 highlighted in red).

(I can share my workings if required).

Please could you help with confirming my loop equations are correct and helping to derive a 4th equation so that I can solve the currents I1-I4. (I can post my workings if needed).

My assignment is a simulation assignment, but I can't build a model with out having my hand calcs correct. #### Attachments

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#### JimB

##### Super Moderator
Attach you picture here, don't link to some external source, it does not work (for me at least).

JimB

#### ZeroSumPlayer

##### New Member
Attach you picture here, don't link to some external source, it does not work (for me at least).

JimB
I have attached now. Thank you.

Anybody?

#### Ratchit

##### Well-Known Member
Hi,

I am working on the below circuit to find; the power dissipated by RL (8Ω resistor), voltage drop across RL and current supplied by the 10 volt battery (V1).

So far I have used Kirchoff's law to the best of my ability to get 3 loop equations but 4 unknowns, I am thrown off by the variable voltage supply V3 = 3Is

In my workings I have used I1=Is for simplicity.

Loop 1

0 =10 - 6I1 - 20I2

Loop 2

0 = 35 I1 - 11 I1 - 6 I3 - 5V

Loop 3

0= 4 I1 - 14 I3 - 18 I4 (V3 = 4I1 highlighted in red).

(I can share my workings if required).

Please could you help with confirming my loop equations are correct and helping to derive a 4th equation so that I can solve the currents I1-I4. (I can post my workings if needed).

My assignment is a simulation assignment, but I can't build a model with out having my hand calcs correct. Assuming all the loop currents have a clockwise direction, you need to learn how to do loop equations. For instance, R2=20 ohms should have the currents from both loop 1 and loop 2, because R2 is common to both loops. You only calculate the loop 2 current. The unknowns are I1, I2, and I3. What is the 4th unknown? Also, do your voltages in a counterclockwise direction against the current direction so you don't run into so many negative signs.

Ratch

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