The diagram shows six 6-$\mu$F capacitors.The capacitance between points a and b is:
A)1 $\mu$F
B)3 $\mu$F
C)4 $\mu$F
D)6 $\mu$F
E)9 $\mu$F

Question

The diagram shows six 6-$\mu$F capacitors.The capacitance between points a and b is: 
A)1 $\mu$F 
B)3 $\mu$F 
C)4 $\mu$F 
D)6 $\mu$F 
E)9 $\mu$F

Quizplus · Accepted Answer

By analyzing the circuit, we can simplify it to the following equivalent circuit:
- Two parallel capacitors with capacitance 6F1F1F1S1μF1F1F10F each, resulting in an equivalent capacitance of 12F1F1F1S1μF1F1F10F.
- Two series capacitors each with capacitance 6F1F1F1S1μF1F1F10F, resulting in an equivalent capacitance of 3F1F1F1S1μF1F1F10F.
- One series capacitor with capacitance 3F1F1F1S1μF1F1F10F and one parallel capacitor with capacitance 6F1F1F1S1μF1F1F10F, resulting in an equivalent capacitance of 2F1F1F1S1μF1F1F7.5F.

Finally, the total capacitance between a and b is the sum of the equivalent capacitances obtained, which is 12F1F1F1S1μF1F1F10F + 3F1F1F1S1μF1F1F10F + 2F1F1F1S1μF1F1F7.5F = 17F1F1F1S1μF1F1F7.5F. However, none of the answer choices match this value exactly, so we choose the closest choice, which is C) 4 F1F1F1S1μF1F1F10F.

The Diagram Shows Six 6- μ\muμ F Capacitors μ\muμ F B)3 μ\muμ F C)4

The Diagram Shows Six 6- $\mu$ F Capacitors $\mu$ F
B)3 $\mu$ F
C)4