Capacitors in Series and Parallel Quiz

PDF page 918: Several capacitors may be connected together in a variety of applications. Multiple connections of capacitors act like a single equivalent capacitor. The total capacitance of this equivalent single capacitor depends both on the individual capacitors and how they are connected. There are two simple and common types of connections, called series and parallel, for which we can easily calculate the total capacitance. Certain more complicated connections can also be related to combinations of series and parallel.

PDF page 918: Note in Figure 19.19 that opposite charges of magnitude flow to either side of the originally uncharged combination of capacitors when the voltage is applied. Conservation of charge requires that equal-magnitude charges be created on the plates of the individual capacitors, since charge is only being separated in these originally neutral devices. The end result is that the combination resembles a single capacitor with an effective plate separation greater than that of the individual capacitors alone. (See Figure 19.19(b).) 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.

PDF page 918: Note in Figure 19.19 that opposite charges of magnitude flow to either side of the originally uncharged combination of capacitors when the voltage is applied. Conservation of charge requires that equal-magnitude charges be created on the plates of the individual capacitors, since charge is only being separated in these originally neutral devices. The end result is that the combination resembles a single capacitor with an effective plate separation greater than that of the individual capacitors alone. (See Figure 19.19(b).) 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.

PDF page 918: Note in Figure 19.19 that opposite charges of magnitude flow to either side of the originally uncharged combination of capacitors when the voltage is applied. Conservation of charge requires that equal-magnitude charges be created on the plates of the individual capacitors, since charge is only being separated in these originally neutral devices. The end result is that the combination resembles a single capacitor with an effective plate separation greater than that of the individual capacitors alone. (See Figure 19.19(b).) 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.

PDF page 919: plate separation . 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 19.19. Solving for gives . The voltages across the individual capacitors are thus , , and . The total voltage is the sum of the individual voltages:

PDF page 920: easier to find than in the series case. To find the equivalent total capacitance , we first note that the voltage across each capacitor is , the same as that of the source, since they are connected directly to it through a conductor. (Conductors are equipotentials, and so the voltage across the capacitors is the same as that across the voltage source.) Thus the capacitors have the same charges on them as they would have if connected individually to the voltage source. The total charge is the sum of the individual charges: 19.67

PDF page 920: easier to find than in the series case. To find the equivalent total capacitance , we first note that the voltage across each capacitor is , the same as that of the source, since they are connected directly to it through a conductor. (Conductors are equipotentials, and so the voltage across the capacitors is the same as that across the voltage source.) Thus the capacitors have the same charges on them as they would have if connected individually to the voltage source. The total charge is the sum of the individual charges: 19.67

PDF page 920: easier to find than in the series case. To find the equivalent total capacitance , we first note that the voltage across each capacitor is , the same as that of the source, since they are connected directly to it through a conductor. (Conductors are equipotentials, and so the voltage across the capacitors is the same as that across the voltage source.) Thus the capacitors have the same charges on them as they would have if connected individually to the voltage source. The total charge is the sum of the individual charges: 19.67

PDF page 921: 19.69 Total capacitance in parallel is simply the sum of the individual capacitances. (Again the “...” indicates the expression is valid for any number of capacitors connected in parallel.) So, for example, if the capacitors in the example above were connected in parallel, their capacitance would be 19.70 The equivalent capacitor for a parallel connection has an effectively larger plate area and, thus, a larger capacitance, as illustrated in Figure 19.20(b).

PDF page 921: 19.69 Total capacitance in parallel is simply the sum of the individual capacitances. (Again the “...” indicates the expression is valid for any number of capacitors connected in parallel.) So, for example, if the capacitors in the example above were connected in parallel, their capacitance would be 19.70 The equivalent capacitor for a parallel connection has an effectively larger plate area and, thus, a larger capacitance, as illustrated in Figure 19.20(b).

PDF page 921: More complicated connections of capacitors can sometimes be combinations of series and parallel. (See Figure 19.21.) To find the total capacitance of such combinations, we identify series and parallel parts, compute their capacitances, and then find the total.

PDF page 921: More complicated connections of capacitors can sometimes be combinations of series and parallel. (See Figure 19.21.) To find the total capacitance of such combinations, we identify series and parallel parts, compute their capacitances, and then find the total.