Calculating Resistance of 25W Lamp & Resistor in Series

[chawki]

Homework Statement

a) Bulb power is 25 W 24 V voltage.
b) 25-watt light bulb and resistor, whose resistance is 19 Ω, connected in series and connected to 24 V DC voltage. In this case, passing within 0.71 A of current.

Homework Equations

a) Calculate the resistance of the lamp.
b) Calculate the resistance of the lamp in this connection.

The Attempt at a Solution

a)
R_lamp = V²/P = 24²/25 = 23.04 Ohms.

b)
Req = R_lamp+R_r
V = Req * I
Req = 24/0.71 = 33.80 Ohms.

R_lamp = Req - R_r
R_lamp = 33.80-19 = 14.8 Ohms ?

 

[anathema]

Hello there, great job on your calculations! Your answer for part a) is correct, the resistance of the lamp is 23.04 Ohms. For part b), you are on the right track but I believe there is a small error in your calculation. The equation for calculating the equivalent resistance in a series circuit is Req = Rlamp + Rr, so the correct answer would be 23.04 + 19 = 42.04 Ohms. This means that the resistance of the lamp in this connection is 42.04 Ohms. Keep up the good work!