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Zorluk: OrtaElectrical Power

A portable communications transceiver connected to a 12 V12\text{ V} direct-current (DC) power source consumes 36 W36\text{ W} of electrical power during operation. What is the effective resistance of the transceiver circuit?

  1. A
    3 Ω3\text{ }\Omega
  2. 4 Ω4\text{ }\OmegaCevap
  3. C
    0.33 Ω0.33\text{ }\Omega
  4. D
    432 Ω432\text{ }\Omega

Cevap

The effective resistance of the transceiver circuit is 4 Ω4\text{ }\Omega.
Electrical power is related to voltage and resistance by the formula P=V2RP = \frac{V^2}{R}. Rearranging this equation to solve for resistance gives R=V2PR = \frac{V^2}{P}. Substituting the given values: R=(12)236=14436=4 ΩR = \frac{(12)^2}{36} = \frac{144}{36} = 4\text{ }\Omega. Alternatively, calculating the current first gives I=PV=3612=3 AI = \frac{P}{V} = \frac{36}{12} = 3\text{ A}, and applying Ohm's Law gives R=VI=123=4 ΩR = \frac{V}{I} = \frac{12}{3} = 4\text{ }\Omega.

Adım Adım Çözüm

1
Identify the given values and appropriate power formula relating power (PP), voltage (VV), and resistance (RR).
P=36 WP = 36\text{ W}, V=12 VV = 12\text{ V}, using P=V2RP = \frac{V^2}{R}.
This formula directly links the known electrical values to the unknown circuit resistance.
2
Rearrange the formula to solve for resistance (RR).
R=V2PR = \frac{V^2}{P}
Isolating the unknown variable allows direct calculation.
3
Substitute the given numerical values and calculate the final resistance.
R=(12 V)236 W=14436=4 ΩR = \frac{(12\text{ V})^2}{36\text{ W}} = \frac{144}{36} = 4\text{ }\Omega
Squaring the voltage and dividing by total power yields the resistance in ohms.

Anahtar Kavram

Relationship between electrical power, voltage, and resistance in DC circuits
Tahmini Süre:1m 0s
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Electrical Power

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