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Capacitor/Inductor: Voltage, power and Energy computation

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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 the voltage.
4. The voltage across a 2 F capacitor is v(t) = 20*e^(-4t) volts. What is the instantaneous power?
5. The current flowing through a 2 H inductor is i(t) = 5*cos(2t) amps. What is the voltage?
6. The charge in a 2 F capacitor varies as q(t) = 20*e^(-4t)*sin(2t) C. What is the voltage?

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Solution Summary

The following posting helps with electricity and magnetism problem. It helps calculate energy, current and voltage. Step by step calculations are given.

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1. Given,
C = 2 F
v = v(pi) = cos(2*pi) = 1 Volt

So, energy in the capacitor = C * v^2 / 2 = 2 * 1^2 / 2 = 1 J

2. Given,
L = 10 H
i = i(pi) = cos(2*pi) = 1 Amps

So, energy in the inductor = L * i^2 / 2 = 10 * 1^2 / 2 = 5 J

3. Given,
L = 1 H
...

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