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 = i**

_{o}sin(wt) where i_{o}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 20**Ω