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 0.330 s, during which it produces an average 0.580 W from an average 3.00 V. (a) What energy does it dissipate? (b) How much charge moves through the lamp? СС (c) Find the capacitance. OF (d) What is the resistance of the lamp?

a) 0.191 J

b) 0.064 C

c) 0.021 F

d) 15.5 ohm

Explanation:

a)

P = Power produced = 0.580 W

t = time interval = 0.330 s

Energy dissipated is given as

E = P t

E = (0.580) (0.330)

E = 0.191 Joules

b)

P = Power produced = 0.580 W

V = Voltage of the source = 3 volts

i = current

Power is given as

P = i V

0.580 = i (3)

i = 0.193 A

Q = amount of charge passed

Amount of charge passed is given as

Q = i t

Q = (0.193) (0.330)

Q = 0.064 C

c)

V = Voltage of the source = 3 volts

Q = Charge passed = 0.064 C

C = Capacitance

Using the equation

Q = CV

0.064 = C (3)

C = 0.021 F

d)

V = Voltage of the source = 3 volts

i = current = 0.193 A

using ohm's law

V = i R

3 = (0.193) R

R = 15.5 ohm