Determine the value of the current and voltage across each resistor impedance

Determine the value of the current and voltage across each resistor impedance, total current and total voltage of the section R1 = 6 ohm R2 = 12 ohm R3 = 2 ohm R4 = 3 ohm R5 = 6 ohm I = 8A

To determine the value of the current I₁, I₂, I₃, I₅, the voltage U₁, U₂, U₃, U₄, U₅ on each resistor, the impedance R, the total current I and the total voltage U of the entire section, it is necessary to take into account that the resistors R₁ and R₂ , as well as R₄ and R₅ are connected in parallel.

Hence, the equalities hold: U₁ = U₂, U₄ = U₅; I₁, ₂ = I₁ + I₂, I₄, ₅ = I₄ + I₅; 1 / R₁, ₂ = 1 / R₁ + 1 / R₂, 1 / R₄, ₅ = 1 / R₄ + 1 / R₅. These sections of the circuit can be conditionally replaced by resistors that provide equivalent resistances R₁, ₂ and R₄, ₅.

The resulting transformed electrical circuit includes a series connection of resistors R₁, ₂, R₃ and R₄, ₅, for which the following relations are fulfilled: U = U₁, ₂ + U₃ + U₄, ₅; I = I₁, ₂ = I ₃ = I₄, ₅; R = R₁, ₂ + R₃ + R₄, ₅.

Calculation of circuit parameters
From the condition of the problem it is known that R₁ = 6 Ohm, R₂ = 12 Ohm, R₃ = 2 Ohm, R₄ = 3 Ohm, R₅ = 6 Ohm, I₄ = 8 A.

Then for R₄ and R₅ we get: U₅ = U₄ = I₄ ∙ R₄ = 8 A ∙ 3 Ohm = 24 V; I₅ = 24 V: 6 Ohm = 4 A; I₄, ₅ = 8 A + 4 A = 12 A; 1 / R₄, ₅ = 1 / (3 Ohm) + 1 / (6 Ohm); R₄, ₅ = 2 Ohm.

For R₃ we get: I = I₃ = I₄, ₅ = 12 A; U₃ = I₃ ∙ R₃ = 12 A ∙ 2 Ohm = 24 V.

For R₁ and R₂ we get: 1 / R₁, ₂ = 1 / (6 Ohm) + 1 / (12 Ohm); R₁, ₂ = 4 Ohm; I₁, ₂ = I₄, ₅ = 12 A; U₁ = U₂ = U₁, ₂ = I₁, ₂ ∙ R₁, ₂ = 12 A ∙ 4 Ohm = 48 V; I₁ = U₁ / R₁ = 48 V: 6 Ohm = 8 A; I₂ = U₂ / R₂ = 48 V: 12 Ohm = 4 A;

For the circuit: U = 48V + 24V + 24V = 96V; R = 4 ohms + 2 ohms + 2 ohms = 8 ohms.

Answer: I₁ = 8 A, I₂ = 4 A, I₃ = 12 A, I₅ = 4 A, U₁ = U₂ = 48 V, U₃ = 24 V, U₄ = U₅ = 24 V, R = 8 Ohm, I = 12 A , U = 96 V.



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