A 3.00 uF and a 5.00 uF capacitor are connected in series cross a 30.0V battery. A 7.00 uF capacitor is then connected in parallel across the 3.00 uF capacitor.
a)Calculate the equivalent capacitance of the circuit
I think the answer is 3.33 uF.
b)Determine the voltage across the 7.00 uF capacitor.
Im not sure how to do this one. Help please?
Thanks
Thanks
ulol tanga!
a) correct
b) 10microC in parallel with 5microfarad.
Same q on each, C=Q/V.
Total capacitance= 3.33micro, Q then equals 3.33micro*30v= 99.9E-6 coulombs
So, in the 5micro, then V=q/C=99.9E-6/5E-6=19.99volts
So the remainder voltage is across the 7uf is 10 volts.
To calculate the equivalent capacitance of the circuit, you need to combine the capacitors properly. In this case, the 3.00 uF and 5.00 uF capacitors are connected in series, so their capacitances add up. The formula for capacitors in series is:
1/Ceq = 1/C1 + 1/C2
where Ceq is the equivalent capacitance, C1 is the capacitance of the first capacitor, and C2 is the capacitance of the second capacitor.
Plugging in the values:
1/Ceq = 1/3.00 uF + 1/5.00 uF
Let's calculate this:
1/Ceq = 0.3333 uF^(-1) + 0.2 uF^(-1)
1/Ceq = 0.5333 uF^(-1)
To get the equivalent capacitance, take the reciprocal:
Ceq = 1 / (0.5333 uF^(-1))
Ceq = 1.875 uF
Therefore, the equivalent capacitance of the circuit is 1.875 uF.
Now, to determine the voltage across the 7.00 uF capacitor, we can use the fact that capacitors in parallel have the same voltage across them. Since the 7.00 uF capacitor is connected in parallel with the 3.00 uF capacitor, they will share the same voltage.
The voltage across the 3.00 uF capacitor can be found using the formula:
Q = CV
where Q is the charge stored on the capacitor, C is the capacitance, and V is the voltage across the capacitor.
Since Q is the same for both capacitors connected in parallel, we can write:
Q = Ceq * Veq
where Ceq is the equivalent capacitance and Veq is the voltage across the 3.00 uF capacitor.
Now we can rearrange this equation to find Veq:
Veq = Q / Ceq
The charge Q can be found using the formula:
Q = CV
where C is the capacitance of the 3.00 uF capacitor and V is the battery voltage (30.0V).
Plugging in the values:
Q = (3.00 uF) * (30.0V)
Q = 90.0 uC
Now we can calculate Veq:
Veq = (90.0 uC) / (1.875 uF)
Veq = 48.0V
Therefore, the voltage across the 7.00 uF capacitor is 48.0V.