Why capacitors are connected in parallel

Larger plate separation means smaller capacitance. It is a general feature of series connections of capacitors that the total capacitance is less than any of the individual capacitances. Figure 1. The magnitude of the charge on each plate is Q. Series connections produce a total capacitance that is less than that of any of the individual capacitors. We can find an expression for the total capacitance by considering the voltage across the individual capacitors shown in Figure 1. Entering the expressions for V 1 , V 2 , and V 3 , we get.

Canceling the Q s, we obtain the equation for the total capacitance in series C S to be. An expression of this form always results in a total capacitance C S that is less than any of the individual capacitances C 1 , C 2 , …, as Example 1 illustrates. Find the total capacitance for three capacitors connected in series, given their individual capacitances are 1.

With the given information, the total capacitance can be found using the equation for capacitance in series. The total series capacitance C s is less than the smallest individual capacitance, as promised. In series connections of capacitors, the sum is less than the parts. In fact, it is less than any individual. Note that it is sometimes possible, and more convenient, to solve an equation like the above by finding the least common denominator, which in this case showing only whole-number calculations is Figure 2a shows a parallel connection of three capacitors with a voltage applied.

Here the total capacitance is easier to find than in the series case. To find the equivalent total capacitance C p , we first note that the voltage across each capacitor is V , the same as that of the source, since they are connected directly to it through a conductor.

The potentials across capacitors 1, 2, and 3 are, respectively, , , and. These potentials must sum up to the voltage of the battery, giving the following potential balance:. Potential V is measured across an equivalent capacitor that holds charge Q and has an equivalent capacitance. Entering the expressions for , , and , we get. Canceling the charge Q , we obtain an expression containing the equivalent capacitance, , of three capacitors connected in series:.

This expression can be generalized to any number of capacitors in a series network. For capacitors connected in a series combination , the reciprocal of the equivalent capacitance is the sum of reciprocals of individual capacitances:. Equivalent Capacitance of a Series Network Find the total capacitance for three capacitors connected in series, given their individual capacitances are , , and.

Strategy Because there are only three capacitors in this network, we can find the equivalent capacitance by using Figure with three terms. Solution We enter the given capacitances into Figure :. Now we invert this result and obtain. Significance Note that in a series network of capacitors, the equivalent capacitance is always less than the smallest individual capacitance in the network. A parallel combination of three capacitors, with one plate of each capacitor connected to one side of the circuit and the other plate connected to the other side, is illustrated in Figure a.

Since the capacitors are connected in parallel, they all have the same voltage V across their plates. However, each capacitor in the parallel network may store a different charge. To find the equivalent capacitance of the parallel network, we note that the total charge Q stored by the network is the sum of all the individual charges:.

On the left-hand side of this equation, we use the relation , which holds for the entire network. On the right-hand side of the equation, we use the relations and for the three capacitors in the network.

In this way we obtain. This equation, when simplified, is the expression for the equivalent capacitance of the parallel network of three capacitors:. This expression is easily generalized to any number of capacitors connected in parallel in the network.

For capacitors connected in a parallel combination , the equivalent net capacitance is the sum of all individual capacitances in the network,. Equivalent Capacitance of a Parallel Network Find the net capacitance for three capacitors connected in parallel, given their individual capacitances are. Solution Entering the given capacitances into Figure yields. Significance Note that in a parallel network of capacitors, the equivalent capacitance is always larger than any of the individual capacitances in the network.

A parallel connection is the most convenient way to increase the total accumulation of electrical charge. The total voltage value does not change. Each capacitor will see the same voltage. The charge of each capacitor is equal and equal to the charge of the corresponding capacitor. The voltage difference across the individual capacitors is equal and equal to the voltage difference across the associated capacitor.

Figure 2. Each is connected directly to the voltage source as if it were alone, so the total capacitance in parallel is just the sum of the individual capacities. To answer your question, capacitors connected in parallel store more energy than capacitors in series. When you connect the capacitors in parallel, you mainly connect the plates to each capacitor. Thus, connecting two identical capacitors in parallel substantially doubles the size of the plates, which substantially doubles the capacitance.

So parallel circuits are power dividers. No single capacitor increases the voltage. However, they can be used in many circuits that produce higher output voltages at the input. Always remember that if power factor is unity or nearly unity then it is good. When a load is connected with an AC supply then it draws current from the source. If the load is inductive then the current drawn by the load will be lag behind the voltage but if the load is capacitive then the current drawn by the load will be lead behind the voltage.

So both lagging or leading current can creates power loss. So we need to keep the power factor near unity. Suppose an inductive load is connected to a source. So it draws the lagging current. In this case, we can compensate the lagging current by flowing leading current. So we have to connect any device or load which can draw leading current such as the capacitor, synchronous motor. If a capacitive load is connected to a source then it draws leading current.