Calculating Resistance of Resistor for 12V/10W Lamp & 24V Accumulator

[chawki]

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

 

[Delphi51]

What quantity is the same throughout a series circuit?
Can you calculate the value of this quantity that the bulb requires?

 

[BAdhi]

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:)

 

[chawki]

P=V²/R_L
R_L=V²/P = 12²/10
R_L= 14.4 Ohms.
we know that when connecting in series, I=I_L=I_R
and also V=V_L+V_R

V_L = R_L * I_L
I_L = 12/14.4 = 0.83Amps.
so, V=R_eq * I
R_eq = V/I
R_L+R_R = V/I
R_R = V/I - R_L
= (24/0.83) - 14.4
= 14.5 Ohms.

PLEASE TELL ME IF IT'S TRUE.

 

[rwisz]

To calculate the resistance of the resistor, we can use Ohm's Law which states that resistance (R) is equal to voltage (V) divided by current (I). In this case, we know the voltage (V) is 24V and the power (P) is 10W. Using the formula P = VI, we can calculate the current (I) to be 0.42A.

Next, we can use the formula R = V/I to calculate the resistance of the resistor. Plugging in the values, we get R = 24V/0.42A = 57.14 ohms. Therefore, a resistor with a resistance of 57.14 ohms should be connected in series with the lamp to ensure proper functioning of the circuit. It is important to note that the power rating of the resistor should also be considered to prevent overheating and potential damage to the circuit.