# 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?

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#### Solution Summary

The solution is a detailed guide for the relationship between voltage and current in capacitor and inductor.

Physics: AC Circuits

(a)

A particular 240V, 50Hz electrical appliance is rated at 2kW and has a lagging power factor of 0.7.

(i)

Determine the appliance's power factor when it is used on a 60Hz supply.

(ii)

Calculate the supply voltage required to maintain the appliance at its rated power when operated off a 60Hz supply.

(b)

When placed in series a coil and capacitor resonate at a frequency of 2251Hz and when placed in parallel they resonate at a frequency of 2228Hz. At parallel resonance it is also found that a current of 5mA flows from the supply when the supply voltage is 25V r.m.s.

Determine the value of the capacitor and the inductance and the resistance of the coil.

I've also attached this problem as a Word document to allow super/subscripts.

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