Engineering Approach for solving voltage across a resistor in circuit?

[InsaneScientist]

Homework Statement

I must solve for the voltage across the resistor labelled R1 in the circuit above. The values given are the resistance of each resistor, the voltage of each voltage source and the current of the current source.

Note: If referring to circuit loops consider them as being numbered from left to right starting in top-left.

Homework Equations

Kirchhoff's Voltage Law
Kirchoff's Current Law
?

The Attempt at a Solution

I'm really not sure what the proper way is to approach this problem. Kirchoff's current and voltage law confuse me. I've done abstract loop analysis in circuits before such as this example:

but we've never had to solve for any values. Also how is the current source I1 in the first picture treated in a loop equation such as the ones in the second picture?

So far I've come up with loop equations for the circuit. I think I can then get a solution for the currents with simultaneous equations and then calculate the voltage through R1 from that. My main problem is I don't know what to do with the current source I1.

 

[berkeman]

I prefer to use the KCL equations. Can you write those for each of the nodes in the circuit?

 

[gneill]

Mesh or nodal analysis is the way to go. If the former, I'd probably choose to convert R7 & I1 into a voltage source with series resistor (i.e. their Thevenin equivalent), thus doing away with the current source.

Yes there will be simultaneous equations to solve.

 

[InsaneScientist]

I prefer to use the KCL equations. Can you write those for each of the nodes in the circuit?

Yes, I could use KCL. Any method is accepted as long as I get the correct answer.

Mesh or nodal analysis is the way to go. If the former, I'd probably choose to convert R7 & I1 into a voltage source with series resistor (i.e. their Thevenin equivalent), thus doing away with the current source.

Yes there will be simultaneous equations to solve.

Thanks. So can I simply change I1 and R7 to a voltage source with Ohm's Law? If I convert it to a voltage source though where in the loop would that voltage source be placed? Adjacent to Loop 4 thus giving me the equation : (I4-I3)R2 + (I4-I2)R5 + (I1*R7) or on it's own in Loop 5?

 

[gneill]

Thanks. So can I simply change I1 and R7 to a voltage source with Ohm's Law?

Essentially, yes. Technically it's the conversion of a Norton model to a Thevenin model.

If I convert it to a voltage source though where in the loop would that voltage source be placed? Adjacent to Loop 4 thus giving me the equation : (I4-I3)R2 + (I4-I2)R5 + (I1*R7) or on it's own in Loop 5?

I1 and R7 are snipped out of the circuit and put in their place is a voltage source of magnitude $I1 R7$ in series with a resistance value of R7. Loop 5 disappears.