If three 5 μF capacitors are connected in parallel, then the net capacitance is
15 μF
Understanding Capacitors in Parallel
When capacitors are connected in parallel, the total capacitance of the combination is the sum of the individual capacitances. This is because connecting capacitors in parallel increases the effective plate area, which in turn increases the capacitance.
In a parallel connection, the voltage across each capacitor is the same, and the total charge stored by the combination is the sum of the charges stored on each capacitor.
Formula for Total Capacitance in Parallel
The formula to calculate the total or equivalent capacitance (\(C_{total}\)) when multiple capacitors (\(C_1, C_2, C_3, ... C_n\)) are connected in parallel is:
\(C_{total} = C_1 + C_2 + C_3 + ... + C_n\)
Calculating the Net Capacitance
We are given three capacitors, each with a capacitance of 5 μF, connected in parallel.
- Capacitor 1 (\(C_1\)) = 5 μF
- Capacitor 2 (\(C_2\)) = 5 μF
- Capacitor 3 (\(C_3\)) = 5 μF
Using the formula for total capacitance in parallel:
\(C_{total} = C_1 + C_2 + C_3\)
\(C_{total} = 5 \mu F + 5 \mu F + 5 \mu F\)
\(C_{total} = (5 + 5 + 5) \mu F\)
\(C_{total} = 15 \mu F\)
Therefore, the net capacitance when three 5 μF capacitors are connected in parallel is 15 μF.
Revision Table: Capacitor Connections
| Feature | Parallel Connection | Series Connection |
|---|---|---|
| Total Capacitance Formula | \(C_{total} = C_1 + C_2 + ... + C_n\) | \(\frac{1}{C_{total}} = \frac{1}{C_1} + \frac{1}{C_2} + ... + \frac{1}{C_n}\) |
| Voltage Relationship | Voltage is the same across each capacitor. | Voltage divides across each capacitor. |
| Charge Relationship | Total charge is the sum of charges on each capacitor. | Charge is the same on each capacitor. |
| Effect on Total Capacitance | Increases total capacitance. | Decreases total capacitance. |
Additional Information on Capacitance
Capacitance is a measure of a capacitor's ability to store an electric charge. It is defined as the ratio of the electric charge stored on a conductor to the difference in electric potential.
The standard unit of capacitance is the Farad (F). However, the Farad is a very large unit, so capacitance values are often given in smaller units like:
- microfarad (μF): 1 μF = \(10^{-6}\) F
- nanofarad (nF): 1 nF = \(10^{-9}\) F
- picofarad (pF): 1 pF = \(10^{-12}\) F
The capacitance of a parallel-plate capacitor depends on the area of the plates, the distance between the plates, and the dielectric material between the plates.
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