What total capacitances can you make by connecting a 4.98 µF and 8.98 µF capacitor together?
series ?
parallel?
Series:
Ct = 4.98*8.98/(4.98+8.98) = 3.20 uF.
Parallel:
Ct = 4.98 + 8.98 = 13.96 uF.
To find the total capacitance when capacitors are connected in series or parallel, we use the following formulas:
1. Series connection:
When capacitors are connected in series, the total capacitance is given by the reciprocal of the sum of the reciprocals of individual capacitances.
Formula: 1/C_total = 1/C1 + 1/C2
2. Parallel connection:
When capacitors are connected in parallel, the total capacitance is equal to the sum of individual capacitances.
Formula: C_total = C1 + C2
For the given capacitors, let's calculate the total capacitance for both series and parallel connections:
1. Series connection:
To find the total capacitance, we use the formula: 1/C_total = 1/C1 + 1/C2
Substituting the given values:
C1 = 4.98 µF and C2 = 8.98 µF
Calculating the reciprocal for each capacitor:
1/C1 = 1/4.98 µF and 1/C2 = 1/8.98 µF
Using the formula:
1/C_total = 1/4.98 µF + 1/8.98 µF
Calculating the sum on the right side of the equation:
1/C_total = (8.98 + 4.98) / (4.98 * 8.98) µF
Simplifying:
1/C_total = 13.96 / 44.6504 µF
Taking the reciprocal on both sides:
C_total = 44.6504 / 13.96 µF
The total capacitance when the capacitors are connected in series is approximately 3.1951 µF.
2. Parallel connection:
To find the total capacitance, we use the formula: C_total = C1 + C2
Substituting the given values:
C1 = 4.98 µF and C2 = 8.98 µF
Using the formula:
C_total = 4.98 µF + 8.98 µF
Calculating the sum on the right side of the equation:
C_total = 13.96 µF
The total capacitance when the capacitors are connected in parallel is 13.96 µF.