Determine the equivalent capacitance of the combination shown when C = 12 nF.
A) 34 nF
B) 17 nF
C) 51 nF
D) 68 nF
E) 21 nF

Question

Determine the equivalent capacitance of the combination shown when C = 12 nF. 
A) 34 nF 
B) 17 nF 
C) 51 nF 
D) 68 nF 
E) 21 nF

Quizplus · Accepted Answer

To start, we can ignore the 4 nF and 9 nF capacitors since they are not connected to the rest of the circuit. Then, we can see that the 6 nF capacitor and the combination of the 8 nF and 16 nF capacitors are connected in parallel. Their equivalent capacitance is:
C_parallel = C_1 + C_2 + C_3 = 6 nF + 8 nF + 16 nF = 30 nF
Next, we can see that the 30 nF and 12 nF capacitors are connected in series. Their equivalent capacitance is:
C_series = (C_1 * C_2) / (C_1 + C_2) = (30 nF * 12 nF) / (30 nF + 12 nF) = 8.571 nF
Finally, we can see that the 8 nF and 16 nF capacitors are also connected in series with the 12 nF capacitor. Their equivalent capacitance is:
C_total = C_series + C_3 = 8.571 nF + 9 nF = 17.57 nF ≈ 17 nF
Therefore, the equivalent capacitance of the combination is approximately 17 nF, which is answer choice B.

Determine the Equivalent Capacitance of the Combination Shown When C