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Quiz 1s. - ECE 205 DE Quiz Sept 4 2009 Name Solution...

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Unformatted text preview: ECE 205 DE Quiz Sept. 4, 2009 Name: Solution grade [10 A battery is charged by a current i(t) shown . Find the electrical charge in the battery at the following times. (a) t=2 sec (3 points) i(t)in (b) t=4 sec (3 points) 1.5 (c) t=6 sec (4 points) t in second m (a) From t=0 to 2 sec l(t)=0.75t A at t=2 sec q(2)=f02 O.75tdt=0.375t2]02=1.5 c (b) From t=2 to 5 sec i(t)=1.5 A at t=4 sec q(4)=q(2) +jz4(1.5)dt=1.5 +1.5t]24=1.5+1.5*(4-2) =4.5 c at t=5 sec q(5)=q(4) +f45 1.5 dt =4.5 +1.5*(5—4)=6 (c) From t=5 to 8 sec i(t)=4-0.5t A at t=6 sec q(6)=q(5)+156(4-0.5t)dt=6+(4t-O.25t2)]56=6+(24-9- 20+6.25)=6+1.25=7.25 C Geometrical Interpretation: (a) At t=25ec q(2)=1.5*2/2=1.5 c (b) At t=4 2 q(4)=1.5*2/2+1.5*(4-2) =4.5 c \, 1.5*(5—2)+ (1.5+1)*1/2 =7.25 C ...
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