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Zorluk: OrtaElectrical Power

An electronics technician measures the operating parameters for four direct-current (DC) subsystems on an avionics test bench. Match each electrical subsystem described on the left with its correct operating power consumption on the right.

  • A relay solenoid with a resistance of 150 Ω150\text{ }\Omega drawing a steady current of 0.4 A0.4\text{ A}24 W24\text{ W}
  • A radio transceiver operating at 28 V28\text{ V} that draws a current of 2.5 A2.5\text{ A}70 W70\text{ W}
  • An instrument panel backlight operating from a 12 V12\text{ V} line with an internal resistance of 24 Ω24\text{ }\Omega6 W6\text{ W}
  • A de-icing heating element with a resistance of 40 Ω40\text{ }\Omega connected across a 120 V120\text{ V} supply360 W360\text{ W}

Cevap

The 150 Ω150\text{ }\Omega solenoid at 0.4 A0.4\text{ A} dissipates 24 W24\text{ W}; the 28 V28\text{ V} transceiver at 2.5 A2.5\text{ A} consumes 70 W70\text{ W}; the 12 V12\text{ V}, 24 Ω24\text{ }\Omega backlight consumes 6 W6\text{ W}; and the 120 V120\text{ V}, 40 Ω40\text{ }\Omega heating element dissipates 360 W360\text{ W}.
Each electrical load's power dissipation is determined by applying the appropriate variation of Watt's Law based on the two given quantities: P=I2RP = I^2 R for the solenoid yielding 24 W24\text{ W}, P=V×IP = V \times I for the transceiver yielding 70 W70\text{ W}, P=V2RP = \frac{V^2}{R} for the instrument backlight yielding 6 W6\text{ W}, and P=V2RP = \frac{V^2}{R} for the de-icing element yielding 360 W360\text{ W}.

Adım Adım Çözüm

1
Calculate power for the 150 Ω150\text{ }\Omega relay solenoid with 0.4 A0.4\text{ A} current.
P=I2R=(0.4)2×150=0.16×150=24 WP = I^2 R = (0.4)^2 \times 150 = 0.16 \times 150 = 24\text{ W}
When current and resistance are known, use Joule's law / Watt's law variation P=I2RP = I^2 R.
2
Calculate power for the 28 V28\text{ V} transceiver drawing 2.5 A2.5\text{ A}.
P=V×I=28×2.5=70 WP = V \times I = 28 \times 2.5 = 70\text{ W}
When voltage and current are known, use the fundamental power formula P=V×IP = V \times I.
3
Calculate power for the 12 V12\text{ V} backlight with 24 Ω24\text{ }\Omega resistance.
P=V2R=12224=14424=6 WP = \frac{V^2}{R} = \frac{12^2}{24} = \frac{144}{24} = 6\text{ W}
When voltage and resistance are known, use the power formula P=V2RP = \frac{V^2}{R}.
4
Calculate power for the 120 V120\text{ V} heating element with 40 Ω40\text{ }\Omega resistance.
P=V2R=120240=1440040=360 WP = \frac{V^2}{R} = \frac{120^2}{40} = \frac{14400}{40} = 360\text{ W}
When voltage and resistance are known, use P=V2RP = \frac{V^2}{R}.

Anahtar Kavram

Electrical power is calculated using the three primary variations of Watt's Law: P=V×IP = V \times I, P=I2RP = I^2 R, and P=V2RP = \frac{V^2}{R}.
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