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damon669
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Homework Statement
a) Calculate the value of the 12V battery
b) Calculate the power dissipated in R_1,R_2 and R.
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Homework Equations
I_1+I_2+I_R=0
The Attempt at a Solution
For the left-hand circuit,
13=12-3I_R+1I_1
(2)
For the right-hand circuit,
14=12-3I_R+2I_2
(3)
Substituting for I_R in equation (2),
13=12-3(-I_1-I_2 )+I_1
13=12+4I_1+3I_2
1=4I_1+3I_2
(4)
Substituting for I_R in equation (3),
14=12-3(-I_1-I_2 )+2I_2
14=12+3I_1+5I_2
2=3I_1+5I_2
(5)
Multiplying equation (4) by 3 and equation (5) by 4 and subtracting to find I_2,
3=12I_1+9I_2
8=12I_1+20I_2
5=11I_2
I_2=5/11 A
Substituting for I_2 in equation (4) to find I_1,
1=4I_1+3(5/11)
I_1=-1/11 A
(9)
Substituting for I_1 and I_2 in (1) to find I_R,
I_R=-(-1/11)-(5/11)
=-4/11 A
=-0.3636 A