A field communication station is powered by a 72\text{ V} direct-current supply connected … — Armed Services Vocational Aptitude Battery (ASVAB)

A field communication station is powered by a $72\text{ V}$ direct-current supply connected across three parallel load branches. The resistance of the first branch is $18\ \Omega$ , the resistance of the second branch is $36\ \Omega$ , and the resistance of the third branch is $72\ \Omega$ . What is the total current, in amperes ( $\text{A}$ ), supplied to the circuit?

Answer: 7 A

Answer

7 A

Each of the three branches is connected directly across the

72\text{ V}

source. Using Ohm's Law (

I = V/R

), the branch currents are

4\text{ A}

2\text{ A}

, and

1\text{ A}

. Adding these currents together yields the total current of

7\text{ A}

Step-by-Step Solution

Calculate the current in the first parallel branch using

I_1 = \frac{V}{R_1}

I_1 = \frac{72\text{ V}}{18\ \Omega} = 4\text{ A}

In a parallel DC circuit, the full supply voltage of

72\text{ V}

appears across every parallel branch.

Calculate the current in the second parallel branch using

I_2 = \frac{V}{R_2}

I_2 = \frac{72\text{ V}}{36\ \Omega} = 2\text{ A}

Applying Ohm's Law to the second branch with its specific resistance.

Calculate the current in the third parallel branch using

I_3 = \frac{V}{R_3}

I_3 = \frac{72\text{ V}}{72\ \Omega} = 1\text{ A}

Applying Ohm's Law to the third branch with its specific resistance.

Add all three individual branch currents together to determine the total current.

I_{\text{total}} = 4\text{ A} + 2\text{ A} + 1\text{ A} = 7\text{ A}

By Kirchhoff's Current Law, the total current leaving the power supply equals the sum of the currents through all parallel branches.

Key Concept

In a parallel circuit, the voltage across each parallel branch is identical to the source voltage, and the total circuit current is the sum of the individual branch currents (

I_{\text{total}} = I_1 + I_2 + \dots + I_n

Alternative Method

Find the total equivalent resistance (

R_{\text{eq}}

) first:

\frac{1}{R_{\text{eq}}} = \frac{1}{18} + \frac{1}{36} + \frac{1}{72} = \frac{4}{72} + \frac{2}{72} + \frac{1}{72} = \frac{7}{72}\ \Omega^{-1}

, so

R_{\text{eq}} = \frac{72}{7}\ \Omega

. Then find total current using

I_{\text{total}} = \frac{V}{R_{\text{eq}}} = \frac{72}{72/7} = 7\text{ A}

Estimated Time:1m 0s

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