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Zorluk: ZorParallel Circuits

A 48 V48\text{ V} direct-current telecommunications power bus supplies electricity to three parallel branches. The first branch draws a current of 2 A2\text{ A}, the second branch contains a load with a resistance of 24 Ω24\ \Omega, and the total current supplied by the power bus is 7 A7\text{ A}. What is the electrical resistance of the third branch, in ohms?

Cevap: 16 ohms

Cevap

The resistance of the third branch is 16 Ω16\ \Omega.
Because the circuit is parallel, the full supply voltage of 48 V48\text{ V} is present across every branch. The second branch with 24 Ω24\ \Omega draws I2=48 V24 Ω=2 AI_2 = \frac{48\text{ V}}{24\ \Omega} = 2\text{ A}. Subtracting the known currents of Branch 1 (2 A2\text{ A}) and Branch 2 (2 A2\text{ A}) from the total current of 7 A7\text{ A} leaves 3 A3\text{ A} flowing through Branch 3. Using Ohm's Law, R3=48 V3 A=16 ΩR_3 = \frac{48\text{ V}}{3\text{ A}} = 16\ \Omega.

Adım Adım Çözüm

1
Calculate the current flowing through Branch 2
I2=VR2=48 V24 Ω=2 AI_2 = \frac{V}{R_2} = \frac{48\text{ V}}{24\ \Omega} = 2\text{ A}
In a parallel circuit, the voltage across each parallel branch is identical to the supply voltage (V1=V2=V3=48 VV_1 = V_2 = V_3 = 48\text{ V}).
2
Calculate the current flowing through Branch 3
I3=Itotal−I1−I2=7 A−2 A−2 A=3 AI_3 = I_{\text{total}} - I_1 - I_2 = 7\text{ A} - 2\text{ A} - 2\text{ A} = 3\text{ A}
The total current entering a parallel network equals the sum of the individual branch currents (Itotal=I1+I2+I3I_{\text{total}} = I_1 + I_2 + I_3).
3
Calculate the resistance of Branch 3
R3=VI3=48 V3 A=16 ΩR_3 = \frac{V}{I_3} = \frac{48\text{ V}}{3\text{ A}} = 16\ \Omega
Applying Ohm's Law (R=VIR = \frac{V}{I}) using the common 48 V48\text{ V} supply voltage and the calculated 3 A3\text{ A} branch current yields the branch resistance.

Anahtar Kavram

In a parallel DC circuit, voltage remains constant across all branches, total current is the algebraic sum of individual branch currents, and branch resistance is determined by Ohm's Law (R=VIR = \frac{V}{I}).
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Konular

Parallel Circuits

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