Chapter 10 Alternating Currents Flashcards
An alternating current (a.c) is defined as
- A current which periodically varies from positive to negative and changes its magnitude continuously with time
- This means the direction of an alternating current varies every half cycle
- The variation of current, or p.d., with time can be described as a sine curve ie. sinusoidal
- Therefore, the electrons in a wire carrying a.c. move back and forth with simple harmonic motion
As with SHM, the relationship between time period T and frequency f of an alternating current is given by:
Peak current (I0), or peak voltage (V0), is defined as:
The maximum value of the alternating current or voltage
Peak current, or voltage, can be determined from the amplitude of the graph
Mains electricity is supplied as alternating current
- Power stations produce alternating current
- This is the type of current supplied when devices are plugged into sockets
The equation representing alternating current which gives the value of the current I at any time t is:
- I = I0 sin(⍵t)
- Where:
- I = current (A)
- I0 = peak current (A)
- ⍵ = angular frequency of the supply (rad s-1)
- t = time (s)
- Note: this a sine function since the alternative current graph is sinusoidal
A similar equation can be used for representing alternating voltage:
V = V0 sin(⍵t)
Where:
V = voltage (V)
V0 = peak voltage (V)
Recall the relation the equation for angular frequency ⍵:
Root-Mean-Square Current
- Root-mean-square (r.m.s) values of current, or voltage, are a useful way of comparing a.c current, or voltage, to its equivalent direct current, or voltage
- The r.m.s values represent the d.c current, or voltage, values that will produce the same heating effect, or power dissipation, as the alternating current, or voltage
- The r.m.s value of an alternating current is defined as:
The value of a constant current that produces the same power in a resistor as the alternating current
- The r.m.s current Ir.m.s is defined by the equation:
- So, r.m.s current is equal to 0.707 × I0, which is about 70% of the peak current I0
- The r.m.s value of an alternating voltage is defined as:
The value of a constant voltage that produces the same power in a resistor as the alternating voltage
- The r.m.s voltage Vr.m.s is defined by the equation:
- Where:
- I0 = peak current (A)
- V0 = peak voltage (V)
- The r.m.s value is therefore defined as:
The steady direct current, or voltage, that delivers the same average power in a resistor as the alternating current, or voltage
- A resistive load is any electrical component with resistance eg. a lamp
Vr.m.s and peak voltage. The r.m.s voltage is about 70% of the peak voltage
Mean Power
- In mains electricity, current and voltage are varying all the time
- This also means the power varies constantly, recall the equations for power:
- Where:
- I = direct current (A)
- V = direct voltage (A)
- R = resistance (Ω)
The r.m.s values means equations used for direct current and voltage can now be applied to
- alternating current and voltage
- These are also used to determine an average current or voltage for alternating supplies
- Recall the equation for peak current:
l0= √2 Ir.m.s
- Therefore, the peak (maximum) power is related to the mean (average) power by:
Pmean= Ir.m.sR
Pmean= P/2
The mean power in a resistive load
is half the maximum power for a sinusoidal alternating current or voltage
- Rectification is defined as:
The process of converting alternating current and voltage into direct current and voltage
Rectification is used in electronic equipment which requires a
direct current
- For example, mains voltage must be rectified from the alternating voltage produced at power stations
There are two types of rectification
- Half-wave rectification
- Full-wave rectification
For half-wave rectification
- The graph of the output voltage Vout against time is a sine curve with the positive cycles and a flat line (Vout = 0) on the negative cycle
- This is because the diode only conducts in the positive direction
For full-wave rectification:
- The graph of the output voltage Vout against time is a sine curve where the positive cycles and the negative cycles are both curved ‘bumps’
The difference between the graphs of full-wave and half-wave rectification
Half-wave rectification consists of a
- single diode
- An alternating input voltage is connected to a circuit with a load resistor and diode in series
- The diode will only conduct during the positive cycles of the input alternating voltage,
- Hence there is only current in the load resistor during these positive cycles
- The output voltage Vout across the resistor will fluctuate against against time in the same way as the input alternating voltage except there are no negative cycles
- This type of rectification means half of the time the voltage is zero
- So, the power available from a half-wave rectified supply is reduced
Full-wave rectification requires a
- bridge rectifier circuit
- This consists of four diodes connected across an input alternating voltage supply
- The output voltage Vout is taken across a load resistor
- During the positive cycles of the input voltage, one terminal if the voltage supply is positive and the other negative
- Two diodes opposite each other that are in forward bias will conduct
- The other two in reverse bias will not conduct
- A current will flow in the load resistor with the positive terminal at the top of the resistor
- During the negative cycles of the input voltage, the positive and negative terminals of the input alternating voltage supply will swap
- The two diodes that were forward bias will now be in reverse bias and not conduct
- The other two in reverse bias will now be in forward bias and will conduct
- The current in the load resistor will still flow in the same direction as before
In full-wave both the positive and negative cycles s, the current in the load resistor is the…
- same
- Each diode pair is the same as in half-wave rectification
- Since there are two pairs, this equates to full-wave rectification overall
- The main advantage of full-wave rectification compared to half-wave rectification is that there is more power available
- Therefore, a greater power is supplied on every half cycle
When A is positive and B is negative, diodes 2 and 3 will conduct and 1 and 4 will not. When A is negative and B is positive, diodes 1 and 4 will conduct and diodes 2 and 3 will not. The current in the load resistor R will flow downwards
Smoothing
- In rectification, to produce a steady direct current or voltage from an alternating current or voltage, a smoothing capacitor is necessary
- Smoothing is defined as:
The reduction in the variation of the output voltage or current
Smoothing works in the following ways:
- A single capacitor with capacitance C is connected in parallel with a load resistor of resistance R
- The capacitor charges up from the input voltage and maintains the voltage at a high level
- As it discharges gradually through the resistor when the rectified voltage drops but the voltage then rises again and the capacitor charges up again
- The resulting graph of a smoothed output voltage Vout and output current against time is a ‘ripple’ shape
A smoothing capacitor connected in parallel with the load resistor. The capacitor charges as the output voltage increases and discharges as it decreases
A smooth, rectified current graph creates a ‘rippling’ shape against time
The amount of smoothing is controlled by the
- capacitance C of the capacitor and the resistance R of the load resistor
- The less the rippling effect, the smoother the rectified current and voltage output
- The slower the capacitor discharges, the more the smoothing that occurs ie. smaller ripples
- This can be achieved by using:
- A capacitor with greater capacitance C
- A resistance with larger resistor R
- Recall that the product RC is the time constant τ of a resistor
- This means that the time constant of the capacitor must be greater than the time interval between the adjacent peaks of the output signal
