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?

Answer 1

When connected in series, the sum of the reciprocals of each capacitance is equal to the reciprocal of the equivalent capacitance.

(1/C₁) + (1/C₂) = (1/C_eq)

If we subtract (1/C₁) from both sides of the equation:

(1/C₂) = (1/C_eq) - (1/C₁)

(1/C₂) = (1/(1.50*10^-5)) - (1/(5.00*10^-5))

Then we multiply the first fraction by 10/10 and the second fraction by 3/3 to obtain a common denominator so we can add the fractions. (We can always multiply by 1) :

(1/C₂) = (10/(1.5*10^-4)) - (3/(1.5*10^-4))

(1/C₂) = (7/(1.5*10^-4))

And take the reciprocal of the result:

C₂ = ((1.5*10^-4)/7) = 2.14 * 10^-5 F