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Zorluk: OrtaElectricity and Magnetism

In an industrial facility, three identical light fixtures are connected in parallel across a constant 120 V120\text{ V} electrical line. If one of the light fixtures burns out and creates an open circuit in its branch, what will happen to the remaining light fixtures and the total current drawn from the line?

  1. A
    All remaining fixtures go out immediately, and the total current drawn from the line drops to zero.
  2. The remaining fixtures stay lit at the same brightness, and the total current drawn from the line decreases.Cevap
  3. C
    The remaining fixtures glow noticeably brighter, and the total current drawn from the line increases.
  4. D
    The remaining fixtures become dimmer, while the total current drawn from the line remains unchanged.

Cevap

The remaining fixtures stay lit at the same brightness, and the total current drawn from the line decreases.
In a parallel circuit, each device is connected across the full source voltage independently. When one fixture burns out, the voltage across the remaining fixtures remains at 120 V120\text{ V}, so their current and brightness stay the same. However, because the total current is the sum of the branch currents (Itotal=I1+I2+I3I_{\text{total}} = I_1 + I_2 + I_3), losing one branch reduces the total current supplied by the line from three branch currents down to two.

Adım Adım Çözüm

1
Analyze voltage across individual branches in a parallel circuit
Each remaining fixture continues to experience the full 120 V120\text{ V} line voltage.
In a parallel circuit, every branch is connected directly across the power source, so removing or opening one branch does not alter the voltage applied to the others.
2
Determine current and power dissipation for each remaining fixture
Individual current I=VRI = \frac{V}{R} and power P=V2RP = \frac{V^2}{R} remain constant, keeping brightness unchanged.
Since both the resistance of each remaining fixture and the supply voltage remain unchanged, the power output of each active lamp does not change.
3
Calculate the effect on total circuit current
Total current drops from Itotal=3IbranchI_{\text{total}} = 3I_{\text{branch}} to Itotal=2IbranchI_{\text{total}} = 2I_{\text{branch}}.
Total current in a parallel circuit is the sum of the individual branch currents (Itotal=I1+I2+I3I_{\text{total}} = I_1 + I_2 + I_3). When one branch opens, its current drops to zero, reducing the total current drawn from the supply.

Anahtar Kavram

Parallel Circuit Branch Independence and Current Summation
Tahmini Süre:1m 0s
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Konular

Electricity and Magnetism

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