An electrical technician is analyzing a perfectly ohmic heating element in a circuit. Duri… — Armed Services Vocational Aptitude Battery (ASVAB)

An electrical technician is analyzing a perfectly ohmic heating element in a circuit. During initial operation, when an unknown voltage $V$ is applied, the element draws a current of $45 \text{ mA}$ . The technician notes that if the applied voltage is increased by exactly $500 \text{ mV}$ , the current drawn by the element increases by $2.5 \text{ mA}$ . Assuming the element's resistance remains completely constant throughout the test, what was the original applied voltage $V$ ?

A
9.5 V
9 VAnswer
C
225 V
D
0.9 V

Answer

9 V

For an ohmic component, resistance (

R

) is constant. This means the change in voltage is directly proportional to the change in current. The resistance can be found using the changes:

R = \Delta V / \Delta I

. After converting to base units,

R = 0.5 \text{ V} / 0.0025 \text{ A} = 200 \, \Omega

. Using Ohm's Law (

V = I \times R

), the original voltage is the original current (

0.045 \text{ A}

) multiplied by this resistance, resulting in

0.045 \text{ A} \times 200 \, \Omega = 9 \text{ V}

Step-by-Step Solution

Identify the relationship between the change in voltage (ΔV) and the change in current (ΔI).

R = \frac{\Delta V}{\Delta I}

For a perfectly ohmic component, the resistance is constant. This means the slope of the voltage-current relationship defines the resistance.

Convert the change values into standard base units (Volts and Amperes) and calculate the resistance.

\Delta V = 500 \text{ mV} = 0.5 \text{ V}

, and

\Delta I = 2.5 \text{ mA} = 0.0025 \text{ A}

R = \frac{0.5 \text{ V}}{0.0025 \text{ A}} = 200 \, \Omega

Standardizing metric prefixes prevents decimal shift errors before applying Ohm's Law.

Apply Ohm's Law to the original state to find the initial voltage.

V = I_{original} \times R = 0.045 \text{ A} \times 200 \, \Omega = 9 \text{ V}

Multiplying the originally measured current by the established component resistance yields the original voltage applied.

Key Concept

Applying Ohm's Law using proportional changes (ΔV and ΔI) while accurately managing metric prefix conversions.

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

Topics

More questions from this topic