Physics >> Electrostatics >> Resistance Containing Circuit
Let a source of alternating be connected to a pure resistance R, suppose the alternating supplied is represented by
E = E0 sin w t
Let I be the current in the circuit at instant t. the potential difference developed across R will be IR. This must be equal to applied at that instant
IR = E = E0 sin w t
Or, I = E0/(R sin w It) = I0 sin w t
Where I0 = E0/R, maximum value of current this the form of alternating current developed.
Comparing I0 = E0/R with ohm’s law equation viz. current = voltage/ resistance we find that resistance to is represented by R-which is the value of resistance to D.C.
Hence behaviour of R in D.C. and A.C. circuits is the same R can reduce A.C. as well as D.C. equally effectively.
It means the minima zero and maxima of alternating voltage and alternating current in a pure resistor over at the same respective times.
Phasor diagram
The analysis of an A.C. circuit is facilitated by the use of a phasor diagram. A phasor is a vector which rotates about the origin with an angular speed w, as shown in
In this diagram peal value of alternating current (I0) and alternating (E0) are represented by arrows called phasor. They are inclined to horizontal axis at w t and rotate in the anticlockwise direction. The lengths of the arrow represent the maximum value of the quantity E0 and I0.
The projections of the arrow on any axis represent the instantaneous value of the quantity. In the sine form projection is taken on the vertical axis and in the cosine form projection is taken on the horizontal axis.
The phase difference between the two alternating quantities is represented by the angle between the two vectors E0 and I0.
In the circuit containing R only current and voltage are in the same phase. Therefore in both phasor Io and E0 are in the same direction making an angle (wt) with OX. This is so for all times. It means that the phase angle between alternating voltage and alternating current through R is zero. Their projections on YOY represent the instanteous value of alternating current and voltage
I = I0 sin wt
And E = E0 sin wt.
Note that as E0 and I0 rotate with frequency w, curves in are generated.
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