Six capacitors are connected as shown in the figure. Six capacitors are connecte
ID: 1900688 • Letter: S
Question
Six capacitors are connected as shown in the figure.
Six capacitors are connected as shown in the figure. (a) IfC3=2.1nF, what doesC2have to be to yield an equivalent capacitance of 5.000 nF for the combination of the two capacitors? (b) For the same values ofC2andC3as in part (a), what is the value ofC1that will give an equivalent capacitance of1.745nF for the combination of the three capacitors? (c) For the same values ofC1,C2, andC3as in part (b), what is the equivalent capacitance of the whole set of capacitors if the values of the other capacitances areC4=1.4nF,C5=2.9nF, andC6=5.5nF? (d) If a battery with a potential difference of 11.7 V is connected to the capacitors as shown in the figure, what is the total charge on the six capacitors? (e) What is the potential drop acrossC5in this case?Explanation / Answer
a) C3=2.1 nF, Ceq 5 nF, (5-2.1)nF=2.9 nF, C2=2.9 nF
b) Ceq=1.745 nF, 1.745=2.9*x/(2.9+x)=1.745*(2.9+x)=2.9*x, 5.0605+1.745*x=2.9*x
5.0605=2.9*x-1.745*x, 5.0605=1.155*x,5.0605/1.155=x, C1=4.382 nF
c) C4+C5+C6=9.8 nF is in series with 1.745 nF
9.8 nF*1.745 nF/(9.8 nF+1.745 nF)1.48 nF=Ceq of system
d) Q=C*V=1.48 nF*11.7 V17.331 nC total charge
e) 17.331 nC/1.745 nF9.932 V drop for right hand side of circuit
11.7-9.932=1.768 V across C5