Question

Two capacitors, C₁ and C₂, are connected in series. C₁ = 5.00 x 10⁻⁵ F, and the equivalent capacitance of the pair is 1.50 x 10⁻⁵ F. What is the capacitance of C₂?

a) 1.00 x 10⁻⁵ F
b) 2.00 x 10⁻⁵ F
c) 3.00 x 10⁻⁵ F
d) 4.00 x 10⁻⁵ F

Answer 1

The capacitance of C2 is 2.14 x 10^-6 F, which is closest to 2.00 x 10^-5 F, making option b the correct answer.

Step-by-step explanation:

When two capacitors, C1 and C2, are connected in series, the equivalent capacitance (Cs) can be found using the formula for series capacitors:

1/Cs = 1/C1 + 1/C2

Given that C1 is 5.00 x 10-5 F and the equivalent capacitance is 1.50 x 10-5 F, we can rearrange the formula to solve for C2:

1/C2 = 1/Cs - 1/C1

1/C2 = 1/(1.50 x 10-5) - 1/(5.00 x 10-5)

1/C2 = 66.67 - 20

1/C2 = 46.67

C2 = 1/(46.67)

C2 = 2.14 x 10-6

Therefore, in terms of the options provided, the capacitance of C2 is closest to 2.00 x 10-5 F (Option b).