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Electromagnetic Waves Notes
ALTERNATING CURRENT
Alternating current. An alternating current is that current whose magnitude changes continuously with time and direction reverses periodically. In contrast to it, a direct current is that current which flows with a constant magnitude in the same direction, as shown in Fig. 7.1.
We know that when a coil is rotated in a magnetic field, an alternating emf is induced in it, which is given by the relation :
ε = εo sin ωt
Suppose this emf is applied to a circuit of resistance R. Then by ohm’s law, the current in the circuit will be
I = = sin ωt or I = Io sin ωt
Thus the current in the circuit varies sinusoidally with time and is called alternating current.
Here
I = instantaneous value of a.c. at any instant t
Io = εo / R = peak or maximum value of a.c. and is called current amplitude.
Amplitude. The maximum value attained by an alternating current in either direction is called its amplitude or peak value and is denoted by Io.
Time period. The tune taken by an alternating current to complete one cycle of its variations is called its time period and is denoted by T. This time is equal to the time taken by the coil to complete one rotation in the magnetic field. As angular velocity of the coil is ω and its angular displacement in one complete cycle is 2 π, so
Time Period = Angular displacement in a completed cycle / Angular velocity or T = 2π / ω
Frequency. The number of cycles completed per second by an alternating current is called its frequency and is denoted by f. The frequency of an alternating current is same as the frequency of rotation of the coil in the magnetic field. Thus
f= 1/T = T = ω / 2π
So an alternating current can be represented as
I = Io sin ωt = Io sin 2 π ft = Io sin 2π/ T t
Figure 7.1 shows the variation of alternating current with time. It rises from 0 to maximum in one direction, then falls to zero and then rises from 0 to maximum in the opposite direction and again falls to zero, thus completing one full cycle.
The alternating current supplied to our houses has a frequency of 50 cps or 50 Hz.
As the alternating current is positive in one half cycle and equally negative in the other half cycle, so its mean value over a complete cycle is zero. We can prove it mathematically also.
2. Prove mathematically that the average value of alternating current over one complete cycle is zero.
Average value of a.c. over one complete cycle. The alternating current at any instant t is given by
I = I0 sin ωt
Assuming the current remains constant for a small time dt, then the amount of charge that flows through the circuit in small time dt will be
dq = Idt = Io sin ωt. dt
The total charge that flows through the circuit in one complete cycle of a.c.,
Thus the average value of a.c. over a complete cycle of a.c. is zero.
Ordinary moving coil galvanometer cannot be used to measure a.c. Ordinary moving coil galvanometer is based on magnetic effect of current which, in turn, depends on direction of current. So it cannot be used to measure a.c. During one half cycle of a.c., its pointer moves in one direction and during next half cycle, it will move in the opposite direction. Now the average value of a.c. over a complete cycle is zero. Even if we measure an alternating current of low frequency, the pointer, will appear to be stationary at the zero position due to persistence of vision.
We can measure a.c. by using a hot-wire ammeter which is based on heating effect of current and this effect is independent of the direction of current.
To measure a.c., we define the mean value of a.c. over half a cycle or its root mean square value.
Alternating Current Notes Class 12 Physics
MEAN OR AVERAGE VALUE OF A.C.
Average value of a.c. It is defined as that value of direct current which sends the same charge in a circuit in the same time as is sent by the given alternating current in its half-time period. It is denoted by
Iav or Im
Relation between average value and peak value of a.c. The value of alternating current at any instant t is given by
I = I0 sin ωt
This current can be assumed to remain constant for a small time dt. Then the amount of charge that flows through the circuit in small time dt is given by
dq = I. dt = I0 sin ωt. dt
The total charge that flows through the circuit, say in the first half cycle, i.e., from t = 0 to t = T / 2 is given by
Thus the mean or average value of an alternating current is 2 / π or 0.637 times its peak value. The similar relation can be proved for the alternating emf, which is
εav = 2/π = 0.637 ε0 .
12th Physics Worksheet
Alternating Current Notes Class 12 Physics
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