Two conductors having net charges of 110.0 mC and
210.0 mC have a potential difference of 10.0 V between
them. (a) Determine the capacitance of the system. (b) What
is the potential difference between the two conductors if the
charges on each are increased to 1100 mC and 2100 mC?
To solve this problem, we can use the formula for capacitance:
C = Q / V
where C is the capacitance, Q is the charge, and V is the potential difference.
(a) To find the capacitance of the system with charges of 110.0 mC and 210.0 mC and a potential difference of 10.0 V, we can substitute these values into the formula:
C = (110.0 mC + 210.0 mC) / 10.0 V
C = 320.0 mC / 10.0 V
C = 32.0 mC/V
Therefore, the capacitance of the system is 32.0 mC/V.
(b) If the charges on each conductor are increased to 1100 mC and 2100 mC, we can calculate the new potential difference between the conductors using the same formula:
C = (1100 mC + 2100 mC) / V
We need to solve for V in this case. Rearranging the equation, we have:
V = (1100 mC + 2100 mC) / C
Substituting the capacitance value from part (a), we have:
V = (1100 mC + 2100 mC) / 32.0 mC/V
V = 3200 mC / 32.0 mC/V
V = 100 V
Therefore, the potential difference between the two conductors, when the charges on each conductor are increased to 1100 mC and 2100 mC, is 100 V.