Elec Class
learn electricity hands-on
Solved exercise · level 4 of 5
Skills: Analyse
Two generators (E1 = 24 V with R1 = 2 Ω, E2 = 6 V with R2 = 2 Ω) supply load R3 = 4 Ω in parallel.
Write Kirchhoff's laws (two loops, one junction) and compute the current in R3.
Parametric exercise: the values change with every draw; these are one example.
The three equations, ΣE − ΣRI = 0 around each loop plus the junction law:
(I) + 24 − 2·I₁ − 4·I₃ = 0
(II) − 6 + 2·I₂ + 4·I₃ = 0
(N) I₁ + I₂ − I₃ = 0
(N) gives I₁ = I₃ − I₂, call it (3), substituted into (I):
+ 24 − 2·(I₃ − I₂) − 4·I₃ = 0
⟺ + 24 − 2 I₃ + 2 I₂ − 4 I₃ = 0
⟺ + 24 + 2 I₂ − 6 I₃ = 0 (4)
Eliminate I₃ between (4) and (II):
(4) × 2: + 48 + 4 I₂ − 12 I₃ = 0
(II) × 3: − 18 + 6 I₂ + 12 I₃ = 0
+ 30 + 10 I₂ = 0, so I₂ = −30 / 10 = −3 A
Work back up:
(II): − 6 + 2·(−3) + 4·I₃ = 0, so I₃ = 3 A
(3): I₁ = I₃ − I₂ = 3 − (−3) = 6 A
Check at the junction: 6 − 3 = 3. A negative current means a source is crossed backwards: it behaves as a load.