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Zorluk: OrtaParallel Circuits

An off-grid solar installation supplies direct-current (DC) power to two ventilation fan circuits connected in parallel across the main distribution bus. The primary intake fan circuit presents a resistance of 40 Ω40\ \Omega, while the secondary exhaust fan circuit presents a resistance of 60 Ω60\ \Omega. What is the total equivalent resistance of these two parallel circuits combined?

  1. A
    100 Ω100\ \Omega
  2. 24 Ω24\ \OmegaCevap
  3. C
    50 Ω50\ \Omega
  4. D
    20 Ω20\ \Omega

Cevap

24 Ω24\ \Omega
For two resistors connected in parallel, the total equivalent resistance (ReqR_{\text{eq}}) is calculated using the product-over-sum formula: Req=R1×R2R1+R2R_{\text{eq}} = \frac{R_1 \times R_2}{R_1 + R_2}. Substituting the circuit values yields Req=40×6040+60=2400100=24 ΩR_{\text{eq}} = \frac{40 \times 60}{40 + 60} = \frac{2400}{100} = 24\ \Omega. In any parallel circuit, the total equivalent resistance must always be less than the resistance of the smallest branch (24 Ω<40 Ω24\ \Omega < 40\ \Omega).

Adım Adım Çözüm

1
Identify the parallel resistance formula for two branch loads
Req=R1×R2R1+R2R_{\text{eq}} = \frac{R_1 \times R_2}{R_1 + R_2}
The equivalent resistance of two parallel resistors is given by their product divided by their sum.
2
Calculate the product of the two branch resistances
40 Ω×60 Ω=2400 Ω240\ \Omega \times 60\ \Omega = 2400\ \Omega^2
Multiplying the individual branch values forms the numerator of the formula.
3
Calculate the sum of the two branch resistances
40 Ω+60 Ω=100 Ω40\ \Omega + 60\ \Omega = 100\ \Omega
Adding the branch values forms the denominator of the formula.
4
Divide the product by the sum to determine equivalent resistance
Req=2400100=24 ΩR_{\text{eq}} = \frac{2400}{100} = 24\ \Omega
Evaluating the quotient provides the total opposition to current flow across the parallel network.

Anahtar Kavram

Parallel Equivalent Resistance
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Parallel Circuits

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