Calculate the resistant of the resistor

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 resistant of the resistor? Thank you.

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 resistant of the resistor?

Power = Volts * Amps
The power of the lamp = 10 watts
The voltage = 12 volts
Amps = 10 ÷ 12 = 0.8333 amps

This is the current that is flowing through the lamp and resistor. The lamp is designed to operate properly at 12 volts. As the 0.8333 amps of current flows through the resistor, the voltage must decrease from 24 volts to 12 volts.

V = I * R
12 = 0.8333 * R
R = 12 ÷ 0.8333 = 14.4 Ω
This is the resistance of the resistor.

OR

A lamp is marked 12V/10W
Power = V^2/R
10 = 12^2/R
R = 14.4 Ω
This is the resistance of the light bulb.

The resistor is in series with the light bulb. So, the total resistance = 14.4 + R
The current is 0.8333 amps

Total voltage = Current * Total resistance
24 = 0.8333 * (14.4 + R)
0.8333 * R = 24 – (0.8333 * 14.4)
0.8333 * R = 12
R = 14.4 Ω

I hope this helps you understand!

the lamp will burn out if connected across 24V
so a resistor must be put in series to reduce the potential drop in the bulb to 12V
from
P = V^2 / R
10 = 144 / R
R = 14.4 ohms
since we want to use half the potential in the bulb and half the potential in the added resistor
the two must be of equal resistance
so
add a 14.4 ohm resistor in series.