What is the equivalent capacitance between points a and b? All capacitors are 5.0 μF.
A)2.6 µF
B)0.19 µF
C)3.0 µF
D)0.33 µF
E)0.13 µF

Question

What is the equivalent capacitance between points a and b? All capacitors are 5.0 μF. 
A)2.6 µF 
B)0.19 µF 
C)3.0 µF 
D)0.33 µF 
E)​0.13 µF

Quizplus · Accepted Answer

To find the equivalent capacitance, we need to simplify the circuit. We can simplify the circuit by combining capacitors that are in series and parallel until we get a single equivalent capacitor between points a and b. 
Firstly, the two capacitors that are in series can be combined into a single capacitor with a capacitance of 2.5 μF:

- The capacitance of two capacitors in series is given by: 
1/C_series = 1/C1 + 1/C2
1/C_series = 1/5 + 1/5 = 2/5
C_series = 5/2 = 2.5 μF

Now we have a circuit with two capacitors in parallel:

- The equivalent capacitance of two capacitors in parallel is given by: 
C_parallel = C1 + C2 
C_parallel = 2.5 + 5 = 7.5 μF

Finally, we have one more capacitor in series with the previous equivalent capacitor. We can add the two capacitances together:

- The capacitance of two capacitors in series is given by: 
1/C_series = 1/C1 + 1/C2
1/C_series = 1/7.5 + 1/5 = 1/3
C_series = 3 μF

Therefore, the equivalent capacitance between points a and b is 3.0 µF (choice C).

What Is the Equivalent Capacitance Between Points a and B