Answer to Question #316011 in Electric Circuits for lia

Question

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​

Answer 1

a)

C =C1+C2+C3+C4+C5 = 10 + 10 + 10 +10 +10 = 50 F

b)

$C=\frac{C1(\frac{C2C3}{C2+C3}+\frac{C4C5}{C4+C5})}{C1+(\frac{C2C3}{C2+C3}+\frac{C4C5}{C4+C5})}=\frac{10(\frac{10\cdot 10}{10+10}+\frac{10\cdot 10}{10+10})}{10+(\frac{10\cdot 10}{10+10}+\frac{10\cdot 10}{10+10})}=5\space F$

c)

$C=C1+C2+C3+\frac{C4C5}{C4+C5}=10+10+10+\frac{10\cdot 10}{10+10}=35\space F$