Having trouble with this one: A capacitor having a capacitance of 10uF is charged by 100v battery. A.)Calculate the charge on the capacitor? B.)calculate the energy stored in the capacitor? C.) the terminals of the capacitor is now disconnected from the batery and the capacitor is now connected across a 20uF capacitor. Calculate the charge on each capacitor and the voltage across each?
Sure! Let's break down the problem step by step.
A.) To calculate the charge on the capacitor, we use the formula Q = C * V, where Q is the charge, C is the capacitance, and V is the voltage.
Given the capacitance (C) of 10uF and the voltage (V) of 100V, we can substitute the values into the formula:
Q = 10uF * 100V = 1,000uC (microcoulombs)
Therefore, the charge on the capacitor is 1,000 microcoulombs.
B.) To calculate the energy stored in the capacitor, we use the formula E = 1/2 * C * V^2, where E is the energy, C is the capacitance, and V is the voltage.
Using the same values from above, we can substitute them into the formula:
E = 1/2 * 10uF * (100V)^2 = 500mJ (millijoules)
Therefore, the energy stored in the capacitor is 500 millijoules.
C.) Now, we have to calculate the charge on each capacitor and the voltage across each capacitor after disconnecting the terminals and connecting a 20uF capacitor in parallel.
We can treat the capacitors as being connected in parallel. When capacitors are connected in parallel, the total capacitance (Ct) is the sum of the individual capacitances. So, Ct = C1 + C2.
Given C1 = 10uF and C2 = 20uF, we can add them together to get:
Ct = 10uF + 20uF = 30uF
Since the capacitors are in parallel, the voltage across them remains the same. Therefore, the voltage across each capacitor is still 100V.
To calculate the charge on each capacitor, we use the formula Q = C * V.
For the first capacitor (C1), with a capacitance of 10uF and a voltage of 100V:
Q1 = 10uF * 100V = 1,000uC (microcoulombs)
For the second capacitor (C2), with a capacitance of 20uF and a voltage of 100V:
Q2 = 20uF * 100V = 2,000uC (microcoulombs)
Therefore, the charge on the first capacitor is 1,000 microcoulombs, and the charge on the second capacitor is 2,000 microcoulombs. Additionally, the voltage across each capacitor remains at 100V.
a,b are standard formulas.
c. 2/3 of q goes to the new capacitor.
then, each voltage can be found C=q/V or V=q/C