A remote weather-monitoring station is powered by a 36\text{ V} direct-current solar batte… — Armed Services Vocational Aptitude Battery (ASVAB)

A remote weather-monitoring station is powered by a $36\text{ V}$ direct-current solar battery bank. Two identical communication transmitters are connected in parallel across the power terminals. If the monitoring station draws a total current of $4\text{ A}$ when both transmitters are operating simultaneously, what is the electrical resistance of each individual transmitter?

A
$9\,\Omega$
B
$4.5\,\Omega$
$18\,\Omega$ Cevap
D
$180\,\Omega$

Cevap

The electrical resistance of each individual transmitter is

18\,\Omega

In a parallel circuit, each identical branch draws an equal share of the total current. With a total current of

4\text{ A}

split evenly across two identical paths, each transmitter draws

2\text{ A}

. Applying Ohm's law (

R = \frac{V}{I}

) across one branch with the full

36\text{ V}

potential difference yields

R = \frac{36\text{ V}}{2\text{ A}} = 18\,\Omega

Adım Adım Çözüm

Calculate the total equivalent resistance of the parallel circuit using Ohm's Law.

R_{\text{eq}} = \frac{V}{I_{\text{total}}} = \frac{36\text{ V}}{4\text{ A}} = 9\,\Omega

The total resistance of the entire circuit relates the total supply voltage to the total current drawn from the battery bank.

Determine the resistance of each individual transmitter from the parallel combination formula.

\frac{1}{R_{\text{eq}}} = \frac{1}{R} + \frac{1}{R} = \frac{2}{R} \implies R = 2 \times R_{\text{eq}} = 2 \times 9\,\Omega = 18\,\Omega

When two identical resistors are connected in parallel, their equivalent resistance is equal to half the resistance of a single component.

Anahtar Kavram

Ohm's law and equivalent resistance in parallel circuits

Alternatif Yöntem

Determine the current per branch directly: because the two transmitters are identical and in parallel across the

36\text{ V}

source, each receives the full supply voltage and carries half the total current (

I_{\text{branch}} = \frac{4\text{ A}}{2} = 2\text{ A}

). Then apply Ohm's law directly to a single branch:

R = \frac{V}{I_{\text{branch}}} = \frac{36\text{ V}}{2\text{ A}} = 18\,\Omega

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