A continuous-duty DC servomotor coil is connected to a 50\text{ V} power line and draws a … — Armed Services Vocational Aptitude Battery (ASVAB)

A continuous-duty DC servomotor coil is connected to a $50\text{ V}$ power line and draws a steady current of $4\text{ A}$ . During a brownout condition, the source voltage drops to $40\text{ V}$ while the internal resistance of the coil remains constant. What is the electrical power dissipated by the servomotor coil under this reduced voltage condition?

A
$40\text{ W}$
$128\text{ W}$ Cevap
C
$160\text{ W}$
D
$200\text{ W}$

Cevap

128\text{ W}

The coil's resistance is determined first using Ohm's Law:

R = \frac{50\text{ V}}{4\text{ A}} = 12.5\text{ }\Omega

. Under the reduced supply voltage of

40\text{ V}

, power dissipation is calculated using

P = \frac{V^2}{R} = \frac{40^2}{12.5} = \frac{1600}{12.5} = 128\text{ W}

. Alternatively, the new current is

I = \frac{40\text{ V}}{12.5\text{ }\Omega} = 3.2\text{ A}

, giving

P = 40\text{ V} \times 3.2\text{ A} = 128\text{ W}

Adım Adım Çözüm

Calculate the constant internal resistance of the coil from initial operating values

R = \frac{V_1}{I_1} = \frac{50\text{ V}}{4\text{ A}} = 12.5\text{ }\Omega

The coil's physical resistance remains constant despite changes in external supply voltage.

Calculate the new current drawn by the coil at the reduced voltage of

40\text{ V}

I_2 = \frac{V_2}{R} = \frac{40\text{ V}}{12.5\text{ }\Omega} = 3.2\text{ A}

By Ohm's Law, reduced voltage across a fixed resistance causes a proportional reduction in current.

Calculate the new electrical power dissipated under the brownout condition

P_2 = V_2 \times I_2 = 40\text{ V} \times 3.2\text{ A} = 128\text{ W}

(or

P_2 = \frac{V_2^2}{R} = \frac{40^2}{12.5} = 128\text{ W}

)

Watt's Law defines power as the product of voltage and current or the square of voltage divided by resistance.

Anahtar Kavram

Electrical power in a resistive load varies with the square of voltage (

P = \frac{V^2}{R}

) when resistance is held constant.

Alternatif Yöntem

Proportional scaling using Watt's Law: Since

P \propto V^2

for constant resistance,

P_2 = P_1 \times \left(\frac{V_2}{V_1}\right)^2 = 200\text{ W} \times \left(\frac{40}{50}\right)^2 = 200 \times 0.64 = 128\text{ W}

Tahmini Süre:1m 30s

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