Ngineering Principles, Electrical Networks, Transients

Module: Engineering Principles ( Electrical Networks )
Topic Title: Transients

1. A capacitor of 12 microfarads capacitance is initially discharged. It is then charged through a 40 kilohms resistor from a 50 volts d.c. supply for 0.2 seconds. Calculate:

i) the capacitor voltage at the end of the 0.2 seconds
ii) the value of the charging current at the same instant
iii) the time constant value of the circuit.

2. A 20 microfarads capacitor is charged to 400 volts. At t 0, a resistor of 12 kilohms is connected across the capacitor.

i) Calculate the voltage remaining across the capacitor after 180 milliseconds.
ii) Calculate the discharge current at this instant.
iii) Calculate the time taken for the voltage to fall to 36.8% of its initial value.

3. A coil having an inductance of 2.5 henrys and a resistance of 40 ohms is switched on to a 60 volt d.c. supply at t 0.

i) Calculate the value of the steady state current eventually reached.
ii) Calculate the value of the current when t 30ms.
iii) Determine the current value when t L/R seconds.

What can you say about the voltage across the coil if the current is suddenly switched off (open circuited)?

4. FIGURE 1 (attached), shows an arrangement where a battery, V, is used to charge an inductor, L, through a resistor, R, when the switch, S, is operated. It may be assumed that the battery is an ideal voltage source, i.e. that it has no internal resistance and that the switch operates instantaneously.

i) Draw to scale waveforms to show the growth and decay of the current in L and the voltages across the two components R and L when the switch is operated to the left at t 0 seconds and returned to the right after 5 seconds.
ii) Calculate the time taken for the current to grow from 10% to 90% of its maximum value (the rise time) and the time taken for it to decay from 90% to 10% of its maximum value (the fall time).

Paper to be written as a question paper, not an essay e.g.

1) i) Answer
ii) Answer etc.

Answers should be as complete as possible, avoid waffle and superfluous padding.

Show sufficient stages in a solution to enable the method of solution to be followed by the tutor.