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voltage and current relationship in capacitor and inductor

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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?

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