An industrial security monitoring loop is powered by a 36\text{ V} DC power supply connect… — Armed Services Vocational Aptitude Battery (ASVAB)

An industrial security monitoring loop is powered by a $36\text{ V}$ DC power supply connected in series with a current-limiting resistor $R_1 = 150\ \Omega$ , an optical sensor module $R_2$ , and a line termination resistor $R_3 = 250\ \Omega$ . When the circuit is active, a voltmeter measures a $12\text{ V}$ drop across the optical sensor module $R_2$ . What is the electrical resistance of the optical sensor module $R_2$ ?

A
$133\ \Omega$
$200\ \Omega$ Answer
C
$400\ \Omega$
D
$600\ \Omega$

Answer

The electrical resistance of the optical sensor module

R_2

200\ \Omega

The correct answer is determined by first finding the remaining voltage across the known resistors (

36\text{ V} - 12\text{ V} = 24\text{ V}

). Dividing this by their combined resistance (

150\ \Omega + 250\ \Omega = 400\ \Omega

) yields a constant loop current of

0.06\text{ A}

. Dividing the sensor's

12\text{ V}

drop by

0.06\text{ A}

gives

200\ \Omega

Step-by-Step Solution

Calculate the combined voltage drop across the known series resistors

R_1

and

R_3

V_{1,3} = V_{\text{total}} - V_2 = 36\text{ V} - 12\text{ V} = 24\text{ V}

In a series circuit, Kirchhoff's Voltage Law dictates that the sum of all individual voltage drops equals the total supply voltage.

Find the sum of the known series resistances.

R_{1,3} = R_1 + R_3 = 150\ \Omega + 250\ \Omega = 400\ \Omega

Resistances in a series path are directly additive.

Determine the common loop current flowing through the circuit.

I = \frac{V_{1,3}}{R_{1,3}} = \frac{24\text{ V}}{400\ \Omega} = 0.06\text{ A}

Current is constant at all points in a series circuit according to Ohm's Law.

Calculate the resistance of

R_2

using its measured voltage drop and the loop current.

R_2 = \frac{V_2}{I} = \frac{12\text{ V}}{0.06\text{ A}} = 200\ \Omega

Applying Ohm's Law (

R = \frac{V}{I}

) to the individual component provides its exact resistance.

Key Concept

Series circuit current constancy and voltage division using Ohm's Law and Kirchhoff's Voltage Law

Alternative Method

Using the voltage divider formula:

\frac{V_2}{V_{\text{total}}} = \frac{R_2}{R_1 + R_2 + R_3} \implies \frac{12}{36} = \frac{R_2}{400 + R_2} \implies \frac{1}{3} = \frac{R_2}{400 + R_2} \implies 400 + R_2 = 3R_2 \implies 2R_2 = 400 \implies R_2 = 200\ \Omega

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Alternative Method

Topics

More questions from this topic