A 2.0-microF capacitor is charged to 50V and then connected in parallel (positive to positive plate) with a 4.0-microF capacitor charged to 100V. (a) What are the final charges on the capacitors? (b) What is the difference across each?
voltages will be equal.
q=C V charge on first: 2E-6&50
charge on second: 4E-6*100 so the charges total is (added)5E-6*100
so in the final condiguration, qt=sum of charges above=5E-6*100
and the voltages are equal.
total capacitance in parallel is 6E-6, so
V=q/C=5E-6*100/6E-6 =500/6 volts
then the final charges on each capacitor is
q1=C1*v
q2=C2*v
q=cu
find the charge of the first capacitor
the find the equivalent capacitance of the parallel and q=c<?>(100)
U(AB)=VA-VB
To find the final charges on the capacitors, we can use the formula Q = CV, where Q is the charge, C is the capacitance, and V is the voltage.
For the 2.0-microF capacitor:
Q1 = C1 * V1
= 2.0 microF * 50V
= 100 microCoulombs
For the 4.0-microF capacitor:
Q2 = C2 * V2
= 4.0 microF * 100V
= 400 microCoulombs
Therefore, the final charges on the two capacitors are 100 microCoulombs and 400 microCoulombs, respectively.
To find the difference in voltage across each capacitor, we can use the formula V = Q/C.
For the 2.0-microF capacitor:
V1 = Q1 / C1
= 100 microCoulombs / 2.0 microF
= 50V
For the 4.0-microF capacitor:
V2 = Q2 / C2
= 400 microCoulombs / 4.0 microF
= 100V
Therefore, the difference in voltage across the two capacitors is 50V and 100V, respectively.
To find the final charges on the capacitors, we can use the principle of conservation of charge. According to this principle, the total charge before and after the capacitors are connected remains the same.
Step 1: Calculate the initial charges on each capacitor:
Q1 = C1 * V1
Q2 = C2 * V2
Where:
Q1 = initial charge on the 2.0-microF capacitor
C1 = capacitance of the 2.0-microF capacitor
V1 = voltage of the 2.0-microF capacitor
Q2 = initial charge on the 4.0-microF capacitor
C2 = capacitance of the 4.0-microF capacitor
V2 = voltage of the 4.0-microF capacitor
Given:
C1 = 2.0 microF
V1 = 50V
C2 = 4.0 microF
V2 = 100V
Substituting the values, we get:
Q1 = 2.0 microF * 50V = 100 microC
Q2 = 4.0 microF * 100V = 400 microC
Step 2: Calculate the total charge before the capacitors are connected:
Total charge = Q1 + Q2 = 100 microC + 400 microC = 500 microC.
Step 3: Calculate the final charges on each capacitor:
Since the total charge remains constant, the final charges will also add up to 500 microC.
Q1_final + Q2_final = 500 microC.
We can solve this equation to find the values of Q1_final and Q2_final.
Now, let's move on to finding the difference across each capacitor.
Step 4: Calculate the final voltage across each capacitor:
Using the formula V = Q / C, we can calculate the final voltage across each capacitor.
V1_final = Q1_final / C1
V2_final = Q2_final / C2
Once we find the final voltage for each capacitor, we can calculate the difference across each capacitor by subtracting the final voltage of one capacitor from the final voltage of the other.
Now, let's calculate the final charges and the differences across each capacitor.