Question

1. The big mall near Sally and Amy's city has extended their operating hours to accommodate the huge crowds expected for the After Thanksgiving Sale. In their eagerness to beat the crowd, Sally forgets to turn off the headlights when she gets out of the car at the mall parking lot. The headlights in her car require 54.0 W of power each, and her 12.0 V car battery is rated at 93.0 A · h. When the two friends come back to the car after a long and successful shopping spree, they find that the car refuses to start as the battery is now completely discharged. How long were they in the mall? Assume that they come out just as the battery dies.

2. An AC voltage source and a resistor are connected in series to make up a simple AC circuit. If the source voltage is given by

V = V₀ sin(2πft)

, find the first time after t = 0 when the instantaneous voltage of 53 Hz AC first reaches the following values.

(a)    

V = V₀/2

(b)    

V = V₀

(c)    

V = 0

Answer 1

1)

Energy consumed by each headlight = 54*time ;

for two headlights, Energy = 2*54*time ;

Battery Can provide = 12*93 W.h = 1116 W.h ;

so 108*time = 1116 ;

time = 10.333 hrs