## Friday, 5 September 2014

### AC THEORY QUESTIONS AND PROBLEMS

AC theory

1. What is meant by the root mean square value of an ac signal?

2. What is the ratio between the peak value of an ac current and its rms value?

3. Calculate (i) the average voltage and (ii) the rms voltage for:
(a) a sine wave of peak value 200 V and frequency 50 Hz
(b) a sine wave of peak value 110 V and frequency 60 Hz
(c) a square wave of peak value 200 V and frequency 50 Hz
(d) a half-wave-rectified sine wave of peak value 200 V and frequency 50 Hz
(e) a half-wave-rectified square wave of peak value 200 V and frequency 50 Hz

4. The current (i) through certain resistor changes with time in the form i = iosin(wt)  where io is the peak value of the current. w is a constant equal to 2πf where f is the frequency of the supply.
If the peak value of the current is 2A, the resistance of the resistor 100 ohm and the frequency of the supply 50 Hz calculate:
(a) the rms value of the current
(b) the peak voltage across the resistor
(c) the current flowing through the resistor at a time t = 0.01 s
(d) on a graph that shows the variation of the current through the resistor with time sketch the variation of voltage across the resistor with time using the same axes

5. An AC supply of 25 V rms is fed to a pure resistor of 100 ohm. Calculate the power used in the resistor.

6. A heater of resistance 10 ohm is connected to a 230 V 50 Hz supply. Calculate:
(a) the average power
(b) the maximum instantaneous power

7. A lamp with a resistance of 5Ω  is connected to a 12 V dc supply and takes a current of 3A. A similar lamp with the same resistance is connected to an ac supply and glows with the same brightness as the dc lamp.
Calculate the peak value of the current in the ac lamp.

8. Calculate the mean power of an ac current of peak value 2A flowing through a resistor of 20Ω