Answer :
Final answer:
In series, the 4.00-pF and 8.00-pF capacitors hold the same charge of 1.068 nC, with voltages across them of 267 V and 134 V, respectively, due to a shared 400 V potential difference.
Explanation:
Capacitors in Series
When capacitors are connected in series, as in the case of the 4.00-pF and 8.00-pF capacitors, they each hold the same charge. This is due to the fact that charge must be conserved, and the same amount of charge that flows onto the positive plate of one capacitor must flow off the negative plate and onto the next one in the series. Using the formula for capacitors in series (1/Ctotal = 1/C1 + 1/C2), where Ctotal is the total capacitance of the combination, the total capacitance can be calculated as follows.
Ctotal = 1 / ((1/4.00) + (1/8.00)) pF = 2.67 pF
The charge (Q) on each capacitor can be determined using the formula Q = C * Vtotal. With a potential difference (Vtotal) of 400 V applied across the series, the charge is calculated as:
Q = 2.67 pF * 400 V = 1.068 nC
The voltage across each capacitor can be found using the formula V = Q / C. For the 4.00-pF and 8.00-pF capacitors, the voltages are:
V4.00-pF = 1.068 nC / 4.00 pF = 267 V
V8.00-pF = 1.068 nC / 8.00 pF = 134 V
