To find out which capacitor has the greatest voltage, we need to understand how capacitors behave when connected in series.
When capacitors are connected in series, the total capacitance (Ct) is given by the reciprocal of the sum of the reciprocals of the individual capacitances (C1, C2, C3):
1/Ct = 1/C1 + 1/C2 + 1/C3
Given that C1 = 1 mF, C2 = 2 mF, and C3 = 3 mF, we can substitute these values into the equation:
1/Ct = 1/1 + 1/2 + 1/3
Calculating this equation, we find:
1/Ct = 3/6 + 2/6 + 2/6
= 7/6
Taking the reciprocal of both sides, we get:
Ct = 6/7
Since the total capacitance is 6/7 mF, we can calculate the voltage across each capacitor using the formula:
V = Q/C
Where V is the voltage, Q is the charge, and C is the capacitance.
Since all three capacitors are connected in the same series circuit, the charge on each capacitor will be the same. Therefore, the voltage across each capacitor will be inversely proportional to its capacitance.
Let's calculate the voltage for each capacitor using the total charge (Q) and the reciprocal of the capacitance (1/C):
Voltage across C1 = Q / C1 = Q / (1/1) = Q / 1 = Q
Voltage across C2 = Q / C2 = Q / (1/2) = Q / (1/2) = 2Q
Voltage across C3 = Q / C3 = Q / (1/3) = Q / (1/3) = 3Q
Since the charge Q is the same for all three capacitors, the voltage is directly proportional to the capacitance. Hence, the capacitor with the greatest voltage is the one with the highest capacitance.
Therefore, the capacitor with the greatest voltage is C3, which has a capacitance of 3 mF.