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Difficulty: MediumParallel Circuits

A 24 V24\text{ V} direct-current (DC) power bus supplies two cooling fans connected in parallel inside a communications cabinet. The primary fan draws a steady branch current of 3 A3\text{ A}, while the secondary fan has an internal resistance of 12 Ω12\text{ }\Omega. What is the total current, in amperes (A\text{A}), delivered by the power bus to the parallel circuit?

Answer: 5 A

Answer

The total current delivered by the power bus is 5 A5\text{ A}.
In a parallel DC circuit, the source voltage (24 V24\text{ V}) is applied directly across each branch. The secondary branch current is found using Ohm's law: I2=24 V12 Ω=2 AI_2 = \frac{24\text{ V}}{12\text{ }\Omega} = 2\text{ A}. Adding the known primary branch current (3 A3\text{ A}) to the secondary branch current (2 A2\text{ A}) yields the total source current of 5 A5\text{ A}.

Step-by-Step Solution

1
Determine the voltage across the secondary branch
Voltage across the secondary fan is 24 V24\text{ V}
In any parallel circuit, every branch experiences the identical full source voltage (Vtotal=V1=V2V_{\text{total}} = V_1 = V_2).
2
Calculate the secondary branch current (I2I_2) using Ohm's law
I2=24 V12 Ω=2 AI_2 = \frac{24\text{ V}}{12\text{ }\Omega} = 2\text{ A}
Ohm's law states that current equals voltage divided by resistance (I=VRI = \frac{V}{R}).
3
Sum all individual branch currents to determine total circuit current
Itotal=3 A+2 A=5 AI_{\text{total}} = 3\text{ A} + 2\text{ A} = 5\text{ A}
Total current in a parallel circuit is the sum of the individual branch currents (Itotal=I1+I2I_{\text{total}} = I_1 + I_2).

Key Concept

Parallel Circuit Current and Ohm's Law
Estimated Time:1m 0s
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Topics

Parallel Circuits

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