5.3.1 Parallel Connection Suppose we have two capacitors C with charge O and C2 with charge that are connected in parallel,as shown in Figure 5.3.2. IAKHAKH-AYI C Ceq-C1+C2 C 9 lrl ArI Figure 5.3.2 Capacitors in parallel and an equivalent capacitor. The left plates of both capacitors Ci and C2 are connected to the positive terminal of the battery and have the same electric potential as the positive terminal.Similarly,both right plates are negatively charged and have the same potential as the negative terminal.Thus, the potential difference Al is the same across each capacitor.This gives 品 6& (5.3.1) These two capacitors can be replaced by a single equivalent capacitor Cwith a total charge Osupplied by the battery.However,since O is shared by the two capacitors,we must have Q=g+Q2=CI△VI+C21△V=(C+C2)IAVI (5.3.2) The equivalent capacitance is then seen to be given by Coa=AV =C+C2 (5.3.3) Thus,capacitors that are connected in parallel add.The generalization to any number of capacitors is Cm=C+C2+C3++Cw=∑C (parallel) (5.3.4) i=l 95.3.1 Parallel Connection Suppose we have two capacitors C1 with charge Q1 and C with charge 2 Q2 that are connected in parallel, as shown in Figure 5.3.2. Figure 5.3.2 Capacitors in parallel and an equivalent capacitor. The left plates of both capacitors C1 and C2 are connected to the positive terminal of the battery and have the same electric potential as the positive terminal. Similarly, both right plates are negatively charged and have the same potential as the negative terminal. Thus, the potential difference | ∆V | is the same across each capacitor. This gives 1 2 1 2 , | | | Q Q C C V = = ∆ ∆V | (5.3.1) These two capacitors can be replaced by a single equivalent capacitor with a total charge Q Ceq supplied by the battery. However, since Q is shared by the two capacitors, we must have Q Q= +1 2 Q = C1 | | ∆V +C2 | | ∆V = ( C1 +C2 )| ∆V | (5.3.2) The equivalent capacitance is then seen to be given by eq 1 2 | | Q C C V = = +C ∆ (5.3.3) Thus, capacitors that are connected in parallel add. The generalization to any number of capacitors is eq 1 2 3 1 (parallel) N N i i C C C C C C = = + + +"+ = ∑ (5.3.4) 9