Resistor needed for a 12V/10W lamp on a 24V power supply

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Homework Statement


A lamp is marked 12V/10W. the lamp is connected to 24V accumulator. in series with lamp you must then connect a resistor.
Calculate the resistance of the resistor.


Homework Equations





The Attempt at a Solution

 
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Discussion

What quantity is the same throughout a series circuit?
Can you calculate the value of this quantity that the bulb requires?
 
to lamp to work properly 12V and current I (which is according to P=IV) has to be provided. So apart from this 12V the rest of the 12V of the supply has to be given to the resistor in series.Now you know the voltage across the resistor and the current (which is same I). Now it's simple:)
 
P=V2/RL
RL=V2/P = 122/10
RL= 14.4 Ohms.
we know that when connecting in series, I=IL=IR
and also V=VL+VR

VL = RL * IL
IL = 12/14.4 = 0.83Amps.
so, V=Req * I
Req = V/I
RL+RR = V/I
RR = V/I - RL
= (24/0.83) - 14.4
= 14.5 Ohms.

PLEASE TELL ME IF IT'S TRUE.