1. Waveform
A waveform is the shape or pattern obtained when an alternating voltage or current is plotted against time.
For a sinusoidal alternating current, the waveform is a sine wave, in which the magnitude and direction of current vary continuously with time.
2. Frequency
Frequency is the number of complete cycles of an alternating quantity occurring in one second.
The unit of frequency is hertz (Hz).
$$f=\frac{1}{T}$$
where:
- f = frequency in Hz
- T = time period of one complete cycle in seconds
3. Average Value
The average value of an alternating quantity is the arithmetic mean of its instantaneous values over a specified period.
For a symmetrical sinusoidal AC waveform, the average value over a complete cycle is zero, because the positive and negative half-cycles cancel each other.
For a rectified waveform, the average value is obtained by considering the rectified current over the complete cycle.
Given:
- AC supply voltage = 110 V RMS
- Resistance = 50 Ω
- Resistance to current in the reverse direction = infinite
- Therefore, current flows through the circuit in only one direction.
Hence, the current is a half-wave rectified sine wave.
Step 1: Calculate the Peak Voltage
The given 110 V is the RMS value of the sinusoidal AC supply.
For a sinusoidal waveform:
$$V_m=\sqrt{2}\times V_{rms}$$
Therefore:
$$V_m=\sqrt{2}\times110$$
$$V_m=155.56\ V$$
Step 2: Calculate the Peak Current
Using Ohm's law:
$$I_m=\frac{V_m}{R}$$
$$I_m=\frac{155.56}{50}$$
$$I_m=3.11\ A$$
Therefore:
$$\boxed{I_m=3.11\ A}$$
This current flows only during one half-cycle because the rectifier blocks current in the opposite direction.
The current waveform is therefore a half-wave rectified sine wave.
(i) Ammeter Readings
Moving Coil Ammeter
A moving coil ammeter responds to the average value of current.
For a half-wave rectified sine wave:
$$I_{avg}=\frac{I_m}{\pi}$$
$$Substituting\:I_{m}=3.11\ A$$
$$I_{avg}=\frac{3.11}{\pi}$$
$$I_{avg}=0.99\ A$$
Therefore, the moving coil ammeter reads:
$$\boxed{I_{MC}=0.99\ A}$$
Thermal Ammeter
A thermal ammeter operates on the heating effect of current and therefore indicates the RMS value of current.
For a half-wave rectified sine wave:
$$I_{rms}=\frac{I_m}{2}$$
Therefore:
$$I_{rms}=\frac{3.11}{2}$$
$$I_{rms}=1.555\ A$$
Hence, the thermal ammeter reads:
$$\boxed{I_{thermal}=1.56\ A}$$
(ii) Form Factor and Peak Factor
Form Factor
The form factor is defined as:
$$Form\ Factor=\frac{RMS\ value}{Average\ value}$$
For a half-wave rectified sine wave:
$$Form\ Factor=\frac{I_m/2}{I_m/\pi}$$
Therefore:
$$Form\ Factor=\frac{\pi}{2}$$
$$\boxed{Form\ Factor=1.57}$$
Peak Factor
The peak factor is defined as:
$$Peak\ Factor=\frac{Maximum\ value}{RMS\ value}$$
For the half-wave rectified sine wave:
$$Peak\ Factor=\frac{I_m}{I_m/2}$$
Therefore:
$$\boxed{Peak\ Factor=2.0}$$
Final Answers
- Supply voltage: 110 V RMS
- Peak voltage: 155.56 V
- Peak current: 3.11 A
- Moving coil ammeter reading: 0.99 A
- Thermal ammeter reading: 1.56 A
- Current waveform: Half-wave rectified sine wave
- Form factor: 1.57
- Peak factor: 2.0
Therefore:
$$\boxed{I_{MC}=0.99\ A}$$
$$\boxed{I_{thermal}=1.56\ A}$$
$$\boxed{Form\ Factor=1.57}$$
$$\boxed{Peak\ Factor=2.0}$$
Note: The values 1.1 A, 1.11 and 1.414 are not applicable to the stated half-wave rectified circuit. For the given circuit, the correct values are 1.56 A, 1.57 and 2.0, respectively.