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Difficulty: MediumParallel Circuits

A 120 V120\text{ V} direct-current power source energizes three parallel branch circuits in an automated conveyor control box. Branch 1 has a resistance of 60 Ω60\ \Omega, while Branch 2 and Branch 3 each have a resistance of 30 Ω30\ \Omega. What is the total current flowing from the power source through the entire circuit?

  1. A
    1 A1\text{ A}
  2. B
    6 A6\text{ A}
  3. 10 A10\text{ A}Answer
  4. D
    12 A12\text{ A}

Answer

10 A10\text{ A}
In a parallel circuit, the voltage across each branch is identical to the source voltage (120 V120\text{ V}). The current in each branch is determined by dividing voltage by resistance: I1=120 V/60 Ω=2 AI_1 = 120\text{ V} / 60\ \Omega = 2\text{ A}, I2=120 V/30 Ω=4 AI_2 = 120\text{ V} / 30\ \Omega = 4\text{ A}, and I3=120 V/30 Ω=4 AI_3 = 120\text{ V} / 30\ \Omega = 4\text{ A}. Summing these branch currents yields a total current of 10 A10\text{ A} (2 A+4 A+4 A=10 A2\text{ A} + 4\text{ A} + 4\text{ A} = 10\text{ A}). Alternatively, calculating equivalent resistance gives 1Req=160+130+130=560=112\frac{1}{R_{\text{eq}}} = \frac{1}{60} + \frac{1}{30} + \frac{1}{30} = \frac{5}{60} = \frac{1}{12}, so Req=12 ΩR_{\text{eq}} = 12\ \Omega, yielding Itotal=120 V12 Ω=10 AI_{\text{total}} = \frac{120\text{ V}}{12\ \Omega} = 10\text{ A}.

Step-by-Step Solution

1
Calculate the individual branch currents using Ohm's Law (I=VRI = \frac{V}{R}).
I1=120 V60 Ω=2 AI_1 = \frac{120\text{ V}}{60\ \Omega} = 2\text{ A}, I2=120 V30 Ω=4 AI_2 = \frac{120\text{ V}}{30\ \Omega} = 4\text{ A}, and I3=120 V30 Ω=4 AI_3 = \frac{120\text{ V}}{30\ \Omega} = 4\text{ A}.
In a parallel circuit, each branch experiences the full source voltage of 120 V120\text{ V}.
2
Sum all individual branch currents to find the total circuit current (Itotal=I1+I2+I3I_{\text{total}} = I_1 + I_2 + I_3).
Itotal=2 A+4 A+4 A=10 AI_{\text{total}} = 2\text{ A} + 4\text{ A} + 4\text{ A} = 10\text{ A}.
By Kirchhoff's Current Law, total current supplied to a parallel network equals the sum of currents through all branches.

Key Concept

Parallel circuit branch current calculation and Kirchhoff's Current Law
Estimated Time:1m 0s
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Topics

Parallel Circuits

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