Answer:
I₁ = 1.07 A
I₂ = 0.44 A
ε = 8.43 V
Explanation:
The currents and voltage can be found using Kirchhoff's circuit laws. The first law is the Current Law, which says that the sum of currents entering and leaving a node is zero. The second law is the Voltage Law, which says that the sum of voltage gains and drops around a loop is zero.
Applying the Current Law at the left node:
I₁ + I₂ = 1.51
Applying the Voltage Law about the top loop:
15.0 − 6.95 I₁ − (5.00) (1.51) = 0
Applying the Voltage Law about the bottom loop:
ε − 2.00 I₂ − (5.00) (1.51) = 0
We now have three equations and three variables. First solve the second equation for I₁.
15.0 − 6.95 I₁ − (5.00) (1.51) = 0
15.0 − 6.95 I₁ − 7.55 = 0
6.95 I₁ = 7.45
I₁ = 1.07 A
Now plug into the first equation to find I₂.
I₁ + I₂ = 1.51
1.07 + I₂ = 1.51
I₂ = 0.44 A
Finally, plug into the third equation to find ε.
ε − 2.00 I₂ − (5.00) (1.51) = 0
ε − 2.00 (0.44) − (5.00) (1.51) = 0
ε = 8.43 V
