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Difficulty: EasyElectrical Power and Watt's Law

An automotive spotlight operates on a 12 V12\text{ V} direct current (DC) electrical system and draws a steady current of 4 A4\text{ A}. How much electrical power is consumed by the spotlight?

  1. A
    3 W3\text{ W}
  2. 48 W48\text{ W}Answer
  3. C
    16 W16\text{ W}
  4. D
    192 W192\text{ W}

Answer

The power consumed by the spotlight is 48 W48\text{ W}.
According to Watt's Law, electrical power (PP) is determined by multiplying voltage (VV) by current (II), using the formula P=V×IP = V \times I. Substituting 12 V12\text{ V} and 4 A4\text{ A} gives P=12 V×4 A=48 WP = 12\text{ V} \times 4\text{ A} = 48\text{ W}.

Step-by-Step Solution

1
Identify the given electrical values from the problem statement.
Voltage (VV) = 12 V12\text{ V}, Current (II) = 4 A4\text{ A}.
Establishing the known quantities determines which form of Watt's Law to apply.
2
Select the appropriate Watt's Law power formula relating power, voltage, and current.
P=V×IP = V \times I
Electrical power in watts equals the product of potential difference in volts and current in amperes.
3
Substitute the values into the formula and calculate.
P=12 V×4 A=48 WP = 12\text{ V} \times 4\text{ A} = 48\text{ W}
Carrying out the multiplication yields the total power dissipated.

Key Concept

Watt's Law relates electrical power (PP) to voltage (VV) and current (II) through the formula P=V×IP = V \times I.
Estimated Time:45s
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Topics

Electrical Power and Watt's Law

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