Resistor in a Sinusoidal AC Circuit

The relationship between the voltage across a resistor and the current passing through it is governed by Ohm's law. When a sinusoidal current flows through resistor R , as shown in Figure 3-4-1, the reference direction of the selected voltage and current is consistent, then according to Ohm's law:

(3-4-1)

If the current i is selected as the reference sinusoidal quantity, then , substituting into the above formula, we have:

The waveforms of current and voltage are shown in Figure 3-4-1.

Figure 3-4-1

When the current of a resistor is a sinusoidal function, the voltage on the resistor is a sinusoidal quantity with the same frequency as the current. The current and voltage are in phase, and their effective values ​​also obey Ohm's law, that is:

(3-4-2)

If expressed in phasor form, we have

(3-4-3)

The above formula is the expression of Ohm's law in complex form. This formula also describes the phase relationship and effective value relationship between the sinusoidal voltage and current on the resistor element. According to formula (3-4-3), the phasor diagram of voltage and current can be drawn, as shown in Figure 3-4-1.