an LC circuit with a 3 uF capacitor and a 3 H inductor has a current I(t)=10*sin(2t) supplied to it . after 2 s, how much charge is stored on a plate of the capacitor?
To find the charge stored on a plate of the capacitor after a given time, we can use the formula:
Q = CV
Where:
Q is the charge stored on the capacitor plates,
C is the capacitance of the capacitor, and
V is the voltage across the capacitor.
In an LC circuit, the voltage across the capacitor (V) can be determined using the equation:
V(t) = I(t) / (wC)
Where:
V(t) is the voltage across the capacitor at time t,
I(t) is the current through the circuit at time t,
C is the capacitance of the capacitor, and
w is the angular frequency of the circuit, given by w = 1 / sqrt(LC).
Given that the current through the circuit is I(t) = 10*sin(2t), and the capacitor has a capacitance of 3 uF (microfarads), we can calculate the angular frequency (w) as follows:
w = 1 / sqrt(LC)
w = 1 / sqrt((3 uF) * (3 H))
Now, we can calculate the voltage across the capacitor at time t = 2s:
V(2s) = I(2s) / (w * C)
V(2s) = 10*sin(2*2) / (w * 3 uF)
Finally, we can calculate the charge stored on a plate of the capacitor using the formula Q = CV:
Q = (3 uF) * V(2s)
Simplifying this equation will give us the answer to how much charge is stored on a plate of the capacitor after 2 seconds in the given LC circuit.