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Difficulty: MediumElectricity and Magnetism

An electrical circuit in an automated test bench connects a 24 V24\text{ V} direct-current power supply to two 12 Ω12\,\Omega heating elements arranged in parallel. What is the total electric current delivered by the power supply to the entire circuit?

  1. A
    1 A1\text{ A}
  2. 4 A4\text{ A}Answer
  3. C
    2 A2\text{ A}
  4. D
    8 A8\text{ A}

Answer

4 A4\text{ A}
In a parallel circuit with two identical 12 Ω12\,\Omega loads, the total equivalent resistance is halved to 6 Ω6\,\Omega. By Ohm's law (I=VRI = \frac{V}{R}), the total current drawn from the 24 V24\text{ V} source is 24 V6 Ω=4 A\frac{24\text{ V}}{6\,\Omega} = 4\text{ A}. Alternatively, each branch draws 24 V12 Ω=2 A\frac{24\text{ V}}{12\,\Omega} = 2\text{ A}, yielding a total current of 2 A+2 A=4 A2\text{ A} + 2\text{ A} = 4\text{ A}.

Step-by-Step Solution

1
Calculate the equivalent resistance of the two identical resistors connected in parallel.
Req=12 Ω2=6 ΩR_{\text{eq}} = \frac{12\,\Omega}{2} = 6\,\Omega
When identical resistors are in parallel, the equivalent resistance equals the resistance of one branch divided by the total number of branches.
2
Apply Ohm's law (I=VReqI = \frac{V}{R_{\text{eq}}}) using the total source voltage and equivalent resistance.
Itotal=24 V6 Ω=4 AI_{\text{total}} = \frac{24\text{ V}}{6\,\Omega} = 4\text{ A}
Ohm's law defines the relationship between total circuit voltage, equivalent resistance, and total current.

Key Concept

Parallel circuit resistance and Ohm's law
Estimated Time:1m 0s
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Topics

Electricity and Magnetism

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