Problem: Determine the equivalent capacitance.
Given:
C1 = 8F
C2 = 8F
C3 = 12F
C4 = 11F
To find: Equivalent capacitance (Ceq)
Solution:
The equivalent capacitance for capacitors in parallel is given by the formula:
1/Ceq = 1/C1 + 1/C2 + 1/C3 + 1/C4
Substituting the given values:
1/Ceq = 1/8F + 1/8F + 1/12F + 1/11F
To add fractions, we need to find a common denominator. The least common multiple (LCM) of 8, 12, and 11 is 264.
1/Ceq = (33/264) + (33/264) + (22/264) + (24/264)
1/Ceq = (33 + 33 + 22 + 24)/264
1/Ceq = 112/264
To simplify the fraction, we can divide both the numerator and denominator by their greatest common divisor (GCD), which is 8.
1/Ceq = (112/8)/(264/8)
1/Ceq = 14/33
Taking the reciprocal of both sides:
Ceq = 33/14
Therefore, the equivalent capacitance (Ceq) is 33/14 F.