Alternative Currents Flashcards
Peak current (I0), or peak voltage (V0), is defined as:
The maximum value of the alternating current or voltage
The equation representing alternating current which gives the value of the currentIat any timetis:
I = I.sin(⍵t)
CIE A Level PhysicsRevision Notes
Home/A Level/Physics/CIE/Revision Notes/21. Alternating Currents/21.1 Properties and Uses of Alternating Current/21.1.1 Alternating Current & Voltage
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21.1.1 Alternating Current & Voltage
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Properties of Alternating Current & Voltage
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 everyhalf cycleThe variation of current, or p.d., with time can be described as a sine curve ie.sinusoidalTherefore, the electrons in a wire carrying a.c. move back and forth withsimple harmonic motion
As with SHM, the relationship betweentime periodT andfrequency 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 theamplitudeof the graph
Graph of alternating current against time with a time period of 20 ms and peak current of 2 A
Mains electricity is supplied as alternating currentPower stations produce alternating currentThis is the type of current supplied when devices are plugged into sockets
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Worked Example
The variation with timetof the output voltageVof an alternating voltage supply is shown in the graph below.Use the graph to calculate the frequency of the supply.
Step 1:
Write down the period-frequency relation
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Step 2:
Calculate the time period from the graph
The time period is the time taken for one complete cycleFrom the graph, this is equal to 0.2 msTherefore,the time period, T = 0.2 ms =0.2 × 10-3s
Step 3:
Substitute into frequency equation
Exam Tip
Remember to double check the units on the alternating current and voltage graphs. These are often shown in the range of milli-seconds (ms) instead of seconds (s) on the x axis.
Using Sinusoidal Representations
The equation representing alternating current which gives the value of the currentIat any timetis:
I = I0sin(⍵t)
I - current
I. - peak current
ω - angular frequency
t- time
An equation which can be used for representing alternating voltage:
V = V.sin(⍵t)
V - voltage
V. -peak voltage
Why do we use r.m.s values
They are a useful way of comparing a.c current or voltage to its equipment direct current or voltage
Root-mean-square (r.m.s) values of current, or voltage, are a useful way ofcomparinga.c current, or voltage, to its equivalent direct current, or voltageThe r.m.s values represent the d.c current, or voltage, values that will produce the sameheating effect, or power dissipation, as the alternating current, or voltage
These are also used to determine anaveragecurrent or voltage for alternating supplies
The r.m.s value of an alternating current is defined as:
The value of a constant current (d.c) that produces the same power in a resistor as the alternating current
I r.m.s = (I.) / (_/2)
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
Vmax = (V.) / (-/2)
The r.m.s value is therefore defined as: (in general)
The steady direct current or voltage that delivers the same average power in a resistor as the alternating current or voltage.
About 70% of peak current/voltage
recall the equations for power:
P = IV = I²R = V²/R
the peak (maximum) power is related to the mean (average) power by:
Pmean = Ppeak / 2
Ppeak = I.² R
= (_/2×Irms)²×R
= 2 Pmean
(Pmean= (Ir.m.s)² × R)
Relation b/w mean power and peak power (in words)
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 currentand voltage
(used in electronic equipment which requires a direct current)
Half-wave rectification
Half-wave rectification requires a single diode and the graph is represented by only the positive cycles
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
During thenegativecycles 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
Advantage of full-wave rectification over half-wave rectification
there ismorepoweravailable
Smoothing is defined as:
The reduction in the variation of the output voltage or current
(Inrectification, to produce a steadydirect current or voltage from analternating currentor voltage, asmoothing capacitoris necessar)
