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A 12-V DC automobile head lamp is to be used on a fishing boat with a 24-V power system. The head lamp is rated at 50 W. A resistor is to be connected in series with the lamp to permit it to operate on 24 V. What should be the resistance and power rating of the resistor?

Answer :

okpalawalter8

Answer:

The  resistance is  [tex]R = 2.88 \ \Omega[/tex]

Explanation:

From the question we are told that

    The  voltage  rating of the headlamp is  [tex]V_1 = 12 \ V[/tex]

     The  voltage of the power system is  [tex]p = 24 \ V[/tex]

     The  power rating of the headlamp  is  [tex]P = 50 W[/tex]

Generally the power which the resistor dissipates is mathematically represented as

      [tex]P = V_L * I[/tex]

=>       [tex]50 = 12 * I[/tex]

=>   [tex]I = 4.1667 \ A[/tex]

Generally the resistance is

      [tex]R = \frac{V_1 }{I}[/tex]

      [tex]R = \frac{12 }{4.1667}[/tex]

      [tex]R = 2.88 \ \Omega[/tex]

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