You have five 10.0 F capacitors. Show all possible connections of all five capacitors to produce an equivalent capacitance of
a. 50.0 F
b. .5 F
c. 35 F
a)
C =C1+C2+C3+C4+C5 = 10 + 10 + 10 +10 +10 = 50 F
b)
C=C1(C2C3C2+C3+C4C5C4+C5)C1+(C2C3C2+C3+C4C5C4+C5)=10(10⋅1010+10+10⋅1010+10)10+(10⋅1010+10+10⋅1010+10)=5 FC=\frac{C1(\frac{C2C3}{C2+C3}+\frac{C4C5}{C4+C5})}{C1+(\frac{C2C3}{C2+C3}+\frac{C4C5}{C4+C5})}=\frac{10(\frac{10\cdot 10}{10+10}+\frac{10\cdot 10}{10+10})}{10+(\frac{10\cdot 10}{10+10}+\frac{10\cdot 10}{10+10})}=5\space FC=C1+(C2+C3C2C3+C4+C5C4C5)C1(C2+C3C2C3+C4+C5C4C5)=10+(10+1010⋅10+10+1010⋅10)10(10+1010⋅10+10+1010⋅10)=5 F
c)
C=C1+C2+C3+C4C5C4+C5=10+10+10+10⋅1010+10=35 FC=C1+C2+C3+\frac{C4C5}{C4+C5}=10+10+10+\frac{10\cdot 10}{10+10}=35\space FC=C1+C2+C3+C4+C5C4C5=10+10+10+10+1010⋅10=35 F
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