Question

Hi all I am hoping someone will be able to help me please?
I have a cuircuit that i need to calculate the current over a resistor using kirchhoffs laws. the equation for loop one is -17-6I_2+41I_1=0 and loop two = -34+10I_2-6I_1=0 although after getting to this point I am now unsure how to contine????

Answer 1

Here is the circuit

Answer 2

there are some mistakes in your equations they should be \[35i _{1}-6i _{3}-17 =0\]\[4i _{2} +6i _{3}-34=0 \] and since you have three unknowns you need three equations to solve. the third equation being Kirchhoff node equation ie,\[i _{1}+i _{2}-i _{3}=0\]

Answer 3

Ok so now I have these three equations where do I go from there? Do I need to simplify them? Thanks Laura

Answer 4

You solve a system of equations like these by systematically eliminating variables from equations by substitution and addition of the equations in pairs until you have an equation in one of the variables. for example use eq 3 to eliminate by substitution i2 from eq 2. then add eqs 1 and 2 to eliminate i3 after appropriately multiplying 1 and 2 by constants so that the coefficients of I2 are the same. solve for I1 Then use the value of i1 to calculate I3 from equation 1 etc.

Answer 5

Ok I have started to do as you say and i have gotten to 4I_2+6(17/41+35/41 I_2 )-34=0 and know I now need to get I_2 on its own but I am a little stuck on how to do this???? any help please? thank you

Answer 6

I just notice that the eq 3 above should be \[i _{1}+i _{3}-i _{2}=0 \] i_1 and i_3 enter the node and i_2 exits. Sorry.

Eliminate i_3 for eq1 and eq 2 using equation 3. Then eliminate i_1 or i_2 from eqs 1 and 2. by subtracting them after getting a common coefficient for the one you wish to eliminate.