An aircraft avionics system is powered by a 28\text{ V} DC supply connected in series with… — Armed Services Vocational Aptitude Battery (ASVAB)

An aircraft avionics system is powered by a $28\text{ V}$ DC supply connected in series with three components: a $40\ \Omega$ indicator lamp, a $70\ \Omega$ current-limiting resistor, and a $30\ \Omega$ monitoring resistor. What is the voltage drop across the $70\ \Omega$ current-limiting resistor?

A
$28\text{ V}$
$14\text{ V}$ Answer
C
$8\text{ V}$
D
$5.6\text{ V}$

Answer

14\text{ V}

The correct answer is

14\text{ V}

. In a series circuit, total resistance equals the sum of the individual resistors:

40\ \Omega + 70\ \Omega + 30\ \Omega = 140\ \Omega

. The circuit current is

I = 28\text{ V} / 140\ \Omega = 0.2\text{ A}

. Multiplying this current by the

70\ \Omega

resistance gives a voltage drop of

0.2\text{ A} \times 70\ \Omega = 14\text{ V}

Step-by-Step Solution

Calculate the total equivalent resistance (

R_{\text{total}}

) of the series circuit.

R_{\text{total}} = 40\ \Omega + 70\ \Omega + 30\ \Omega = 140\ \Omega

In a series circuit, total resistance is the algebraic sum of all individual resistances.

Determine the common circuit current (

I

) using Ohm's Law.

I = \frac{V_{\text{total}}}{R_{\text{total}}} = \frac{28\text{ V}}{140\ \Omega} = 0.2\text{ A}

Current remains constant through every component along a single series path.

Calculate the voltage drop across the

70\ \Omega

resistor (

V_{70\Omega}

V_{70\Omega} = I \times R = 0.2\text{ A} \times 70\ \Omega = 14\text{ V}

Applying Ohm's Law (

V = I \times R

) to the specific component yields its proportional voltage drop.

Key Concept

Series Circuit Resistance and Voltage Division

Alternative Method

Use the voltage divider formula directly:

V_{70\Omega} = 28\text{ V} \times \left(\frac{70\ \Omega}{40\ \Omega + 70\ \Omega + 30\ \Omega}\right) = 28\text{ V} \times \frac{70}{140} = 28\text{ V} \times 0.5 = 14\text{ V}

Estimated Time:1m 0s

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Step-by-Step Solution

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