Three identical 10 micro farad capacitors are connected in series across a 100V DC supply...calculate the total charge
Ct = 10uF/3 = 3.33 uF.
Qt = Q1 = Q2 = Q3 = Ct*V = 3.33 * 100 =
333 Micro coulombs.
To calculate the total charge in a series circuit, we can use the equation:
Q = C_eq * V
Where:
Q is the total charge,
C_eq is the equivalent capacitance of the series capacitors, and
V is the applied voltage.
In a series circuit, the equivalent capacitance is given by the reciprocal of the sum of the reciprocals of individual capacitances.
For three identical capacitors in series, the equation becomes:
C_eq = 1 / (1/C + 1/C + 1/C)
Let's calculate the equivalent capacitance:
C_eq = 1 / (1/10uF + 1/10uF + 1/10uF)
= 1 / (30uF/10uF)
= 1 / 3
= 0.33 microfarads (rounded to two decimal places)
Now, we can calculate the total charge:
Q = C_eq * V
= 0.33uF * 100V
= 33 microcoulombs (rounded to two decimal places)
Therefore, the total charge across the three capacitors in series is 33 microcoulombs.
To calculate the total charge, we will use the formula Q = CV, where Q represents the charge, C represents the capacitance, and V represents the voltage.
In this case, we have three identical capacitors connected in series, which means the effective capacitance is given by the formula:
1/C_total = 1/C1 + 1/C2 + 1/C3
Since all three capacitors have the same capacitance, we can rewrite the equation as:
1/C_total = 1/C + 1/C + 1/C = 3/C
Simplifying further:
C_total = C/3
Now we can use this effective capacitance value to calculate the total charge:
Q = C_total * V
Given that C = 10 microfarads and V = 100V, we substitute these values into the equation:
Q = (10 microfarads / 3) * 100V
Since 1 microfarad is equal to 10^(-6) farads, we convert the capacitance to farads:
Q = (10 * 10^(-6) farads / 3) * 100V
Simplifying:
Q = (10 * 10^(-6) farads / 3) * (100 / 1) V
Q = 1/3 * (10 * 100 * 10^(-6)) Coulombs
Calculating further:
Q = 1/3 * (10 * 100 * 10^(-6)) Coulombs
Q = 1/3 * (10 * 10^(-4)) Coulombs
Q = 1/3 * (10^(-3)) Coulombs
Q = 10^(-3) / 3 Coulombs
Q ≈ 0.333 Coulombs
Therefore, the total charge is approximately 0.333 Coulombs.