A 10\text{ k}\Omega linear potentiometer is wired as a variable rheostat by tying the cent… — Armed Services Vocational Aptitude Battery (ASVAB)

A $10\text{ k}\Omega$ linear potentiometer is wired as a variable rheostat by tying the center wiper (terminal 2) directly to outside terminal 3. If the control shaft is set to $25\%$ of its total travel starting from terminal 1 toward terminal 3, what is the effective resistance measured between terminal 1 and the combined terminal 2/3 connection?

A
$7.5\text{ k}\Omega$
$2.5\text{ k}\Omega$ Cevap
C
$1.875\text{ k}\Omega$
D
$25\text{ k}\Omega$

Cevap

2.5\text{ k}\Omega

A potentiometer wired with its wiper connected to one outer terminal functions as a two-terminal variable resistor (rheostat). Setting the shaft to

25\%

rotation from terminal 1 creates a

2.5\text{ k}\Omega

resistance path between terminal 1 and terminal 2. Because terminal 2 is strapped to terminal 3, the remaining

7.5\text{ k}\Omega

section of the resistive element is completely bypassed by the short, leaving an effective resistance of

2.5\text{ k}\Omega

Adım Adım Çözüm

Determine the resistance of the active resistive track between terminal 1 and the wiper (terminal 2).

R_{1-2} = 0.25 \times 10\text{ k}\Omega = 2.5\text{ k}\Omega

Linear potentiometers divide resistance directly in proportion to shaft travel percentage from the reference end.

Analyze the state of the remaining track segment between the wiper (terminal 2) and terminal 3.

R_{2-3} = 7.5\text{ k}\Omega

is short-circuited.

Connecting terminal 2 directly to terminal 3 creates a zero-resistance path across this section, bypassing it entirely.

Calculate the total effective resistance between terminal 1 and the joined 2/3 terminal.

R_{\text{eff}} = 2.5\text{ k}\Omega

Current flows through the unshorted

R_{1-2}

segment and exits via the combined wiper/terminal 3 connection.

Anahtar Kavram

Rheostat Wiring and Potentiometer Track Division

Tahmini Süre:45s

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