Odpowiedź:
1. Obwód równoległy z R₁, R₂ i R₃
I₁ = U / R₁
I₁ = U / 2Ω [A]
I₂ = U / R₂
I₂ = U / 2Ω [A]
I₃ = U / R₃
I₃ = U / 2Ω [A]
I = I₁ + I₂ + I₃
I = U / 2Ω + U / 2Ω + U / 2Ω [A]
I = 3U / 2Ω [A]
U = U₁ = U₂ = U₃ [V]
Rₓ = U / I = U / (3U / 2Ω)
Rₓ = [tex]\frac{2}{3}[/tex] Ω
albo inaczej:
1 / Rₓ = 1 / R₁ + 1 / R₂ + 1/ R₃
1 / Rₓ = 1 / 2Ω + 1 / 2Ω + 1/ 2Ω
1 / Rₓ = 3 / 2Ω
czyli
Rₓ = [tex]\frac{2}{3}[/tex] Ω
2. Obwód równoległy z R₁ i R₂
I₁ = U / R₁
I₁ = U / 2Ω [A]
I₂ = U / R₂
I₂ = U / 2Ω [A]
I = I₁ + I₂
I = U / 2Ω + U / 2Ω [A]
I = 2U / 2Ω [A]
I = U / 1Ω [A]
U = U₁ = U₂ [V]
Rₓ = U / I = U / (2U / 2Ω)
Rₓ = 1 Ω
albo inaczej:
1 / Rₓ = 1 / R₁ + 1 / R₂
1 / Rₓ = 1 / 2Ω + 1 / 2Ω
1 / Rₓ = 2 / 2Ω
czyli
Rₓ = 1 Ω
3. Obwód mieszany z R₁, R₂, R₃, R₄, R₅, R₆ i R₇
1 / R₃₋₄₋₅ = 1 / R₃ + 1 / R₄ + 1 / R₅
1 / R₃₋₄₋₅ = 1 / 2Ω + 1 / 2Ω + 1/ 2Ω
1 / R₃₋₄₋₅ = 3 / 2Ω
czyli
R₃₋₄₋₅ = [tex]\frac{2}{3}[/tex] Ω
Rₓ = R₁ + R₂ + R₃₋₄₋₅ + R₆ + R₇
Rₓ = 2Ω + 2Ω + [tex]\frac{2}{3}[/tex] Ω + 2Ω + 2Ω
Rₓ = 8[tex]\frac{2}{3}[/tex] Ω
I = ε / Rₓ
I = ε / 8[tex]\frac{2}{3}[/tex] Ω [A]
I = 3ε / 26 Ω [A]
I = I₁ = I₂ = I₆ = I₇
I = I₁ = I₂ = I₆ = I₇ = 3ε / 26 Ω [A]
I₃ = I₄ = I₅ = I / 3
I₃ = I₄ = I₅ = I / 3 = (3ε / 26 Ω) / 3 [A]
I₃ = I₄ = I₅ = I / 3 = (ε / 26 Ω) [A]
U₁ = U₂ = U₆ = U₇ [V]
U₁ = U₂ = U₆ = U₇ = I * 2Ω [V]
U₁ = U₂ = U₆ = U₇ = (3ε / 26 Ω) * 2Ω [V]
U₁ = U₂ = U₆ = U₇ = 3ε / 13 [V]
U₃₋₄₋₅ = I * R₃₋₄₋₅
U₃₋₄₋₅ = (3ε / 26 Ω) * [tex]\frac{2}{3}[/tex] Ω [V]
U₃₋₄₋₅ = ε / 13 [V]
ε = U = U₁ + U₂ + U₃₋₄₋₅ + U₆ + U₇
ε = U = 3ε / 13 + 3ε / 13 + ε / 13 + 3ε / 13 + 3ε / 13
ε = U = 12ε / 13 + ε / 13
ε = U = 13ε / 13
ε = U = ε [V]
Wyjaśnienie: