TWO series capacitors ( one 1 microFarad, the other of unknown value ) are charged from a 12 Voltage source. The 1 microFarad capacitor is charged to 8 Voltage and the other to 4 Voltage. What is the value of the unknown capacitor?
I don't see why they both don't charge to the full 12 V, if they are charged separately or in parallel.
What you seem to be talking about is charging them together in Series. In that case, the sum of the voltages is the supply voltage (12 V), and they both hold the same charge.
Therefore Q = C1*V1 = C2*V2
1 uF * 8 V = x * 4 V
x is the unknown capactitance, and you can solve for it.
x = (8/4) * 1 uF = 2 uF = 2*10^-6 F
(uF stands for microFarads)
Thankyou drwls.
To find the value of the unknown capacitor, we can use the concept of equivalent capacitance in series.
When capacitors are connected in series, the total capacitance (Ceq) is given by the reciprocal of the sum of the reciprocals of the individual capacitances.
Let C1 be the capacitance of the known capacitor (1 microFarad) and C2 be the capacitance of the unknown capacitor.
So, the total capacitance can be written as:
1 / Ceq = 1 / C1 + 1 / C2
Since the voltage across capacitors in series is divided such that the sum of the voltage drops across each capacitor is equal to the source voltage, we can use this information to solve the equation.
The voltage across the known capacitor (C1) is given as 8 Volts, and the voltage across the unknown capacitor (C2) is given as 4 Volts.
Therefore, we can write the equation as:
4 / Ceq = 1 / 1 + 1 / C2
Simplifying the equation:
4 / Ceq = 1 + 1 / C2
Multiplying both sides of the equation by Ceq:
4 = Ceq + Ceq / C2
Since Ceq = C1 + C2, we can rewrite the equation as:
4 = 1 + 1 / C2 + C1 / C2
Substituting the known values:
4 = 1 + 1 / C2 + 1 / (1 microFarad)
Simplifying further, we can convert the microFarad to Farad by dividing it by 1,000,000:
4 = 1 + 1 / C2 + 1 / (1 × 10^-6 Farad)
Combining the terms:
4 = 1 + 1 / C2 + 1,000,000 C2
Multiplying through by C2:
4 C2 = C2 + 1 + 1,000,000
Rearranging the terms:
C2 - 4 C2 = 1,000,001 - 1
-3 C2 = 1,000,000
Dividing both sides by -3:
C2 = -1,000,000 / 3
The value of the unknown capacitor (C2) is approximately -333,333 Farads.
To find the value of the unknown capacitor, we need to apply the principles of capacitors in series.
In a series circuit, the total capacitance (Ct) is given by the reciprocal of the sum of the reciprocals of the individual capacitances (C1 and C2):
1/Ct = 1/C1 + 1/C2
Let's use this formula to solve the problem.
Given:
C1 = 1 microFarad
V1 = 8 Volts
C2 = unknown
V2 = 4 Volts
Using the given information, we can plug in the known values into the voltage-capacitance equation:
V1 = Q1/C1
8 = Q1/(1 * 10^-6)
Q1 = 8 * 10^-6 Coulombs
V2 = Q2/C2
4 = Q2/C2
Q2 = 4 * C2 Coulombs
Now, since the series capacitors share the same charge, we can equate the charges:
Q1 = Q2
8 * 10^-6 = 4 * C2
C2 = (8 * 10^-6) / 4
C2 = 2 * 10^-6 Farads
Therefore, the value of the unknown capacitor is 2 microFarads.