1. Three parallel plate capacitors are connected in series. These capacitors hav
ID: 1267568 • Letter: 1
Question
1.
Three parallel plate capacitors are connected in series. These capacitors have identical geometries. However, they are filled with three different materials. The dielectric constants of these materials are 3.05, 5.14, and 7.00. It is desired to replace this series combination with a single parallel plate capacitor. Assuming that this single capacitor has the same geometry as each of the other three capacitors, determine the dielectric constant of the material with which it is filled.
2.
In a heart pacemaker, a pulse is delivered to the heart 75 times per minute. The capacitor that controls this pulsing rate discharges through a resistance of 1.80 106?. One pulse is delivered every time the fully charged capacitor loses 62.0% of its original charge. What is the capacitance of the capacitor?
Explanation / Answer
a)
Given 3 capacitors have same geometries i.e same area and length ,so only thing different is dielectric constant ,so
1/K =1/K1 +1/K2 +1/K3 =1/3.05 +1/5.14+1/7
K=1.503
b)
Time
t=60/75 =0.8 s
given
Q=(1-0.62)Qo=0.38Qo
since
Q=Qoe-t/T
0.38=e-0.8/T
ln(0.38)=-0.8/T
T=0.8268 s
since
T=RC
=>C=T/R =0.8268/1.8*106
C=4.5933*10-7 F or 0.46 uF or 460 nF
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