voltage and current relationship in capacitor and inductor

Please see the attached file for full problem description.

1. The voltage across a 5 uF capacitor is v(t) = 10sin(377t) V. What current flows through the capacitor?

2. The current flowing through a 5 F capacitor i(t) = 5e^(-2t) A. Write down the voltage and plot it for seconds. The capacitor is initially uncharged.

3. A 1 F capacitor is charged to that the initial voltage across it is 1 V. If the current flowing through the capacitor is
i(t) = 4e^(-3t) A, what is the voltage?

4. A 1 F capacitor is charged to that the initial voltage across it is 1 V. If the current flowing through the capacitor is
i(t) = 4e^(-3t) A, what is the instantaneous power?

5. A 1 F capacitor is charged so that the initial voltage across it is 1 V. If the current flowing through the capacitor is
i(t) = 4e^(-3t) A, what is the energy in the capacitor for the first two seconds (take the initial time to be zero)?

6. A 40 ohms resistor is in series with a 1/10 F capacitor. How much time must elapse before the voltage across the capacitor drops to 37% of its initial value?

7. A current i(t) = 3e^(-2t) A is flowing through a 2 H inductor. What is the voltage across the inductor? Plot it for
0 < t <= 2 seconds.

8. What is the mutual inductance for a transformer constructed out of inductors with 6 H and 4 H respectively?

9. A 12 H inductor is in series with a 1000 ohms resistor. How much time is required for the current flowing through the inductor to drop to 37% of its initial value?

10. The voltage across an inductor with 100 windings is 200 V and the voltage across a second, linked inductor is 5 V. How many windings does the second inductor have?

(See attached file for full problem description)
---
Problem 2. Current through 1uF capacitor is given as i(t) = 4 cos (wt) where w corresponds to the frequency of 1 MHz. What is the expression for the voltage on the capacitor?
Problem 3. The same current i(t) = 4 cos (wt), at the frequency of 1 MHz, is flowing through

Please help with the following problem. Step by step calculations are given.
An L-C circuit consists of a 60.0 mH inductorand 250 µF capacitor. The initial Charge in the capacitor is 6.00 µC and initial current in the inductor is zero.
a) What is the maximum voltage across the capacitor?
b) What is the maximum current

Please help with the following problem. Provide step by step calculations for each.
1. What is the energy in a 2 F capacitor at t = pi seconds if v(t) = cos(2t) ?
2. What is the energy in a 10 H inductor at t = pi seconds if i(t) = cos(2t) ?
3. The current flowing through a 1 H inductor is i(t) = 10*cos(20t) amps. Find th

See attached for full description of problems.
1. Determine the Laplace transform of ?(t) = + 5e^-4t + 12sin 3t.
2. If v(t) = 10e^-t/3 for some circuit, when does the voltage fall to 37% of its initial value?
3. Let ?(t) = sin2t. What is the Laplace transform of d? / dt ?
4. The charge in a certain capacitor varies as q =

The problem is in the right column of the attached page. There are two # 11's so it is the one on the right.
See attached file for full problem description.
You have a 200 ohms resistor, a 0.400 H inductor, and a 6.00 uF capacitor. Suppose you take the resistor andinductorand make a series circuit with a voltage source th

1. An inductor is connected to the terminals of a battery that has an emf of 12.0V and negligible internal resistance. The current is 4.86mA at 0.725 ms after the connections is completed. After a long time the current is 6.45 mA. What is
a) The resistance R of the inductor?
b) The inductance L of the inductor?

Please provide detailed steps in finding the answers.
1) Find the Laplace transform of e^(−3t) cos 4t.
2) Find the inverse Laplace Transform of s/(s^2 - 1).
3) The transfer function for a circuit is H(s) = (s-1)/((s-1)^2 + 4). What is the natural response of the system? Is it stable?
4) The natural response of

A circuit consists of a sine wave signal generator and a reactive component (L or C). The output of the generator is a sine wave with a peak amplitude of 8.8 volts at a frequency of 10.0 kHz.
a. The generator is connected to an inductor with L = 10.0 mH. What is the rms current flowing in the inductor?
b. The generator

Determine and plot as a function of time the current through a component if the voltage across it has the waveform shown in Figure and the component is a:
a) Resistor R = 7 Ω
b) Capacitor C = 0.5 μF
c) Inductor L = 7 mH