Find the capacitance of a single equivalent capacitor that when connected to the battery would store the same charge. Solution: (IV-9 #1) __________ F (IV-9 #2) Find the charge on each of the capacitors. Solution: From the arguments on the previous page, the all have the same charge, Q, which can be calculated from: Q = __________ C (IV-9 #3) Find the across each capacitor. ∆V Solution: is given by Q/C for the capacitor. ∆V (IV-9 #4) Note that = + + ∆Vbattery ∆V1 ∆V2 ∆V3. Capacitors Connected In Parallel The three capacitors sketched at the right are connected IN PARALLEL with a battery of voltage across its terminals. Using the same ideas as we did for the capacitors connected ∆Vb in series, namely, that the sum of the around a closed loop as zero, we can see that in ∆Vs loop 1: = where is the potential difference across capacitor C1. Similarly, in loop ∆Vb ∆V1 ∆V1 2: = and in loop 3: = where and are the potential differences ∆V1 ∆V2 ∆V2 ∆V3 ∆V2 ∆V3 across C2 and C3, respectively. Thus we see that the potential difference (or voltage) across a bunch of capacitors connected in parallel is the same. Note that since the capacitance is given by C = Q/∆V, then if then the charges . Here we have the main difference between capacitors connected in series and those connected in parallel. For n capacitors in series: Q1 = Q2 = Q3 = . . . = Qn For n capacitors in parallel: = = = . . . = ∆V1 ∆V2 ∆V3 ∆Vn In our circuit note that after the battery has been connected and the situation has become static, the total charge, Q, that has been supplied by the battery is Q = Q1 + Q2 + Q3 Where Q1, Q2, and Q3 are the charges on each capacitor.
Find the capacitance of a single equivalent capacitor that when connected to the battery would store the same charge. Solution: (IV-9 #1) __________ F (IV-9 #2) Find the charge on each of the capacitors. Solution: From the arguments on the previous page, the all have the same charge, Q, which can be calculated from: Q = __________ C (IV-9 #3) Find the ∆V across each capacitor. Solution: ∆V is given by Q/C for the capacitor. (IV-9 #4) Note that ∆Vbattery = ∆V1 + ∆V2 + ∆V3. Capacitors Connected In Parallel The three capacitors sketched at the right are connected IN PARALLEL with a battery of voltage ∆Vb across its terminals. Using the same ideas as we did for the capacitors connected in series, namely, that the sum of the ∆Vs around a closed loop as zero, we can see that in loop 1: ∆Vb = ∆V1 where ∆V1 is the potential difference across capacitor C1. Similarly, in loop 2: ∆V1 = ∆V2 and in loop 3: ∆V2 = ∆V3 where ∆V2 and ∆V3 are the potential differences across C2 and C3, respectively. Thus we see that the potential difference (or voltage) across a bunch of capacitors connected in parallel is the same. Note that since the capacitance is given by C = Q/∆V, then if then the charges . Here we have the main difference between capacitors connected in series and those connected in parallel. For n capacitors in series: Q1 = Q2 = Q3 = . . . = Qn For n capacitors in parallel: ∆V1 = ∆V2 = ∆V3 = . . . = ∆Vn In our circuit note that after the battery has been connected and the situation has become static, the total charge, Q, that has been supplied by the battery is Q = Q1 + Q2 + Q3 Where Q1, Q2, and Q3 are the charges on each capacitor.