Kaksi vastusta R1= 12 Ω ja R2= 13 Ω on kytketty rinnan. Edellisen systeemin rinnalle on kytketty sarjaan vastukset R3= 13 Ω ja R4= 9 Ω. Laske näiden neljän vastuksen muodostaman systeemin kokonaisresistanssi. Anna vastaus kahden desimaalin tarkkuudella ilman yksikköä.Two resistors R1= 12 Ω ja R2= 13 Ω are connected parallel. These resistors are connected parallel with resistors R3= 13 Ω ja R4= 9 Ω connected in series. Calculate the total resistance of this four resistor system. Give the answer with two decimal accuracy without unit.

Question

Kaksi vastusta R1= 12 Ω ja R2= 13 Ω on kytketty rinnan. Edellisen systeemin rinnalle on kytketty sarjaan vastukset R3= 13 Ω ja R4= 9 Ω. Laske näiden neljän vastuksen muodostaman systeemin kokonaisresistanssi. Anna vastaus kahden desimaalin tarkkuudella ilman yksikköä.Two resistors R1= 12 Ω ja R2= 13 Ω are connected parallel. These resistors are connected parallel with resistors R3= 13 Ω ja R4= 9 Ω connected in series. Calculate the total resistance of this four resistor system. Give the answer with two decimal accuracy without unit.

BlackTom AI · Accepted Answer

Kaksi R1 ja R2 vastusta ovat kytketty rinnankytkimeen, joten niiden yhdistetty resistanssi lasketaan parallel-hetkellä: R12,eq = (R1 * R2) / (R1 + R2) = (12 * 13) / (12 + 13) = 156 / 25 = 6.24 Ω.

Seuraavaksi yhdistetään R3 ja R4 sarjaan: R34,eq = R3 + R4 = 13 Ω + 9 Ω = 22 Ω.

Nyt nämä kaksi ryhmää ovat kytketty again rinnakkain toisiaan, eli koko verkon vastus saadaan parallel-laskulla: R_total = (R12,eq * R34,eq) / (R12,eq + R34,eq) = (6.24 * 22) / (6.24 + 22).

Lasketaan ensin osoittaja: 6.24 * 22 = 137.28. Yhteenlaskettu nimittäjä: 6.24 + 22 = 28.24. Jako antaa R_total = 137.28 / 28.24 ≈ 4.858... Ω.

Pyydetty tarkkuus on kahden desimaalin, joten pyöristetään: 4.86.

Jos haluat tarkistaa: 1/R_total = 1/6.24 + 1/22 ≈ 0.160256 + 0.045455 ≈ 0.205711, jolloin R_total ≈ 1 / 0.205711 ≈ 4.858 Ω, joka on 4.86 kahden desimaalin tarkkuudella.

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