Question

A lamp in a child's Halloween costume flashes based on an RC discharge of a capacitor through its resistance. The effective duration of the flash is 0.280 s, during which it produces an average 0.710 W from an average 3.00 V.

A) What energy does it dissipate?
B) How much charge moves through the lamp?
C) Find the capacitance.
D) What is the resistance of the lamp?

Answer 1

A. 0.199 J

B. 0.0663 C

C = 0.0221 F

D. 12.68 ohms

Step-by-step explanation:

From the question:

time duration, t = 0.28 seconds

Average power, P = 0.71 W

Average voltage, V = 3 V

A) Energy is given as:

E = P * t

=> E = 0.71 * 0.28 = 0.199 J

B) Electrical energy is also given as:

E = qV

where q = charge

=> q = E / V

∴ q = 0.199 / 3 = 0.0663 C

C) Capacitance is given as charge over voltage:

C = q / V

=> C = 0.0663 / 3 = 0.0221 F

D) Electrical power, P, can also be given as:

P =
`V^2 / R`

where R = resistance

=> R =
`V^2 / P`

R =
`3^2 / 0.71 = 9 / 0.71 = 12.68 ohms`