Help!! problem about capacitance and inductance...
please help me...
god bless u all...
1.) A capacitance of 2.0 micro-Farad with an initial charge Qo is switched into a series circuit consisting of a 10.0 ohms resistance.
Find Qo if the energy dissipated in the resistance is 3.6 mJoules.
2.) An inductance of 4.0 milli-Henries has a voltage
V= ( 2.0e^ (-10^ (3t) ) (v). Obtain the maximum stored energy. When will the current be zero??
1) When is the energy dissipated measured? RC circuits discharge with a specific rate.
2) Inductances have energy stored in the magnetic field in accordance with 1/2 L i^2, where i is current. Because current and voltage are 90 degrees out of phase (pure L circuit), it is not possible to go further with this problem.
1.) To solve this problem, we need to use the concept of energy stored in a capacitor and the relationship between charge, capacitance, and voltage.
First, we know that the energy dissipated in the resistance is given by the formula: Energy = (1/2) * Q^2 / C, where Q is the charge on the capacitor and C is the capacitance. In this case, the energy is given as 3.6 mJoules.
We can rearrange the formula to solve for Q: Q = sqrt(2 * Energy * C).
Substituting the given values, we have: Q = sqrt(2 * 3.6 * 10^-3 * 2 * 10^-6).
Evaluating this expression, we find that Q = 0.012 coulombs. Therefore, the initial charge on the capacitor (Qo) is 0.012 coulombs.
2.) To find the maximum stored energy in an inductor, we need to use the formula: Energy = (1/2) * L * I^2, where L is the inductance and I is the current.
Given the voltage V(t) = 2 * e^(-10^3t) volts, we can differentiate it with respect to time to find the current I(t). Differentiating the given voltage, we have: I(t) = -20 * e^(-10^3t) amps.
Substituting this current into the energy formula, we have: Energy = (1/2) * 4 * 10^-3 * (-20 * e^(-10^3t))^2.
To find the maximum stored energy, we differentiate the energy with respect to time and set it equal to zero. Differentiating the energy, we have: dE(t) / dt = -160 * e^(-10^3t) * (-20 * e^(-10^3t)) = 3200 * e^(-2 * 10^3t).
Setting this expression equal to zero, we find: 3200 * e^(-2 * 10^3t) = 0.
Taking the natural logarithm of both sides, we have: -2 * 10^3t = ln(0).
Since the natural logarithm of zero is undefined, there is no real solution for when the current will be zero. The current will never be zero in this case.