Two different examples are given below. The first is explained in detail. The second is more concise. Both examples involve the circuit shown in the diagram at right. The voltage across capacitor C is the only given value. The goal of the two examples is to determine the voltages across capacitors A and D.
Kirchoff's Loop Law states that the voltage rises and drops around any closed loop must sum to zero. A closed loop is a path around the circuit that starts and stops at the same location. The circuit diagram that is shown at right is identical to the one above except that a particular closed loop has been highlighted. The loop is colored green except for capacitor D, which is colored red. Capacitor D is colored differently to remind you that you are trying to determine the voltage across it.
To apply Kirchoff’s Loop Law, imagine ‘walking’ around the closed loop in one direction or the other. It doesn’t matter whether you walk clockwise or counterclockwise around the loop. It also doesn’t matter where in the loop you start because you will stop where you started. For the sake of this example, imagine that you start next to the bottom of capacitor C and walk clockwise around the highlighted loop. Before returning to your starting point you will walk past capacitor C, then capacitor D. Hence, according to Kirchoff’s Loop Law:
VC + VD = 0
where VC and VD represent the voltages across C and D respectively. For this equation to be true, one of these voltages must be a rise (i.e., positive) and the other a drop (i.e., negative). Because we are only trying to find the magnitude of the voltage across D, it doesn’t matter which is which. The absolute values of the two voltages are equal:
|VC| = |VD| = 14V.
Capacitors C and D in the circuit above are connected together in parallel.
Two capacitors are connected in parallel when both ends of one are connected to both ends of the other.
In more complicated circuits, it can be difficult to identify which capacitors are in parallel. One way to do so is by applying the following alternate definition of parallel.
Two capacitors are connected in parallel if a closed loop exists that contains the two capacitors and nothing else.
Whenever two capacitors are connected in parallel, the voltages across them are equal. This was proven above through an application of Kirchoff’s Loop Law.
The circuit at right is identical to the circuit in the previous example, but this time a different closed loop is highlighted. As before, most of the loop is colored green except for one red capacitor. The red capacitor is colored differently to remind you that you are trying to determine the direction of the voltage across it.
Two capacitors are connected in parallel if a closed loop exists that contains the two capacitors and nothing else.