Ohm’s law for AC systems
Let us say that our imaginary ideal generator (voltage source) in Figure 1, is supplying a load with a resistance of R ohms. Note that ‘R’ is a fixed or constant value and does not change with respect to time, hence we use the upper case.
For an AC system, the Ohm’s law can be written as below:
e = i R or i = e / R … (3)
In AC systems, the Ohm’s law holds good at any given instant time!
Example 1
An ideal AC sinusoidal voltage source with a peak of 340 V is supplying a resistance load of 100 Ω at a frequency of 50 Hz. Calculate the value of the voltage and current at 0.028 seconds and 1.011 seconds. The voltage is given to be 0 V at time t = 0.
Using Equation (2),
e = Em sin(ωt)
where Em = 340 V
ω = 2πf = 2 x π x 50 = 314.16 rad/s
We have, e = 340 sin(314.16 t) V
(a) At t = 0.028 s
e = 340 sin(314.16 x 0.028) = 199.84 V
Using Ohm’s law as given in Equation (3),
i = e / R = Em sin(ωt) / R
= 340 sin(314.16 x 0.028) / 100
= 199.84 / 100 = 1.9984 A
(b) At t = 1.011 s
e = 340 sin(314.16 x 1.011) = –105.3 V
Using Ohm’s law as given in Equation (3),
i = e / R = Em sin(ωt) / R
= 340 sin(314.16 x 1.011) / 100
= -105.3 / 100 = -1.053 A
A negative value of voltage indicates that the voltage is opposite to the reference polarity. Similarly, a negative value of current indicates that the current is flowing in a direction opposite to the reference direction. For example, it is traditional to assume that the current flows out of the positive terminal. The actual current in this case is flowing into the positive terminal!
