A system of four capacitors is connected across a 90-V voltage source as shown in the figure.What is the equivalent capacitance of this system?
A)1.5 μF
B)15 μF
C)3.6 μF
D)3.3 μF

Question

A system of four capacitors is connected across a 90-V voltage source as shown in the figure.What is the equivalent capacitance of this system? 
A)1.5 μF 
B)15 μF 
C)3.6 μF 
D)3.3 μF

Quizplus · Accepted Answer

The capacitors in parallel can be combined using the formula Cp = C1 + C2, and the capacitors in series can be combined using the formula Cs = (C1 * C2)/(C1 + C2). By combining the two capacitors on the left in parallel, we get Cp1 = 6 μF. By combining the two capacitors on the right in parallel, we get Cp2 = 1.5 μF. Then, the two capacitors Cp1 and Cp2 are in series, and combining them gives: 
Cs1 = (Cp1 * Cp2)/(Cp1 + Cp2) = (6 * 1.5)/(6 + 1.5) = 1.2 μF
Finally, the two capacitors Cs1 and C3 are in parallel, giving: 
Cp3 = Cs1 + C3 = 1.2 + 2.1 = 3.3 μF
Therefore, the equivalent capacitance of the system is 3.3 μF.

A System of Four Capacitors Is Connected Across a 90-V