If the heads of multiple capacitors are connected, such a combination is adding capacitors in parallel. Just like resistor parallel combination, it provides multiple paths for the flow of current. The voltage across each capacitor is the same for each voltage source and the total charge is the summation of all individual charges of capacitors.
As the voltage of each capacitor is the same, so mathematically
$I_{T}=i_{1}+i_{2}+i_{3}\ldots +i_{n} \quad \dots (1)$
By the definition of current, the current is
$i=\frac{Q}{t}$
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The equation (1) will become
$\frac{Q_{T}}{t}=\frac{Q_{1}}{t}+\frac{Q_{2}}{t}+\ldots
+\frac{Q_{3}}{t} \quad \dots (2)$
Suppose the whole parallel combination of capacitors is connected for a specific duration of time, t. Now dividing the equation (2) by t, we will get
$Q_{T}=Q_{1}+Q_{2}+\ldots +Q_{n} \quad \dots (3)$
We know that charge of a capacitor depends upon the capacitance and voltage, as follow
$Q=CV$
Put it to the equation (3), to get
$C_{T}E=C_{1}V_{1}+C_{2}V_{2}+\ldots +C_{n}V_{n} \quad \dots (4)$
As the connection is parallel and we know that voltage across each component is will be the same as source voltage i.e.
$E=v_{1}+v_{2}+v_{3}\ldots +v_{n} $
Now put it to the equation (4), and we get
$C_{T}v=C_{1}v+C_{2}v+\ldots +C_{n}v -(5) $
Finally, dividing the equation (5) by the voltage v to get the total capacitance of the parallel combination i.e.
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$C_{T}=C_{1}+C_{2}+\ldots +C_{n}$
Capacitors in Parallel Calculator
The capacitors in the parallel calculator calculate the total capacitance with the capacitance formula. It takes three capacitor values and calculates the total capacitance.
Capacitors in Parallel Summary :
- Provides multiple paths for charging and discharging current.
- The heads and tails of all capacitors are connected.
- The charge of each capacitor depends upon the capacitance and may be different.
- Adding more capacitors in series will increase the resultant capacitance.
- The voltage across each capacitor remains the same.