Prism Glow - Electronics - EEES - Chapter 2 - Alternating Currents and Voltages

Resistance is defined as a parameter that causes a voltage drop directly proportional to the current that passes through it. That property is expressed as Ohm's Law. This effect holds equally true for both direct current (DC) circuits and for alternating current (AC or time varying) circuits.
We earlier defined an instantaneous current to be where is the instantaneous current at any time and is the maximum value or amplitude. The quantity is expressed in radians per second and is the angular velocity. When that current exists in a simple series circuit the instantaneous voltage across the resistance is .
In a purely resistive circuit voltage and current are in phase. This is indicated on a graph by showing the curves crossing the x-axis at the same points. For convenience of calculations, most often the origin is arbitrarily chosen as one of the crossing points. The equations just presented imply that condition.
However, a different time origin is often necessary for many calculations. Given here that we consider the current to have a phase angle , these equations will look like this: and . That will cause the peak voltage to be .

Electronics > EEES > Chapter 2 - Alternating Currents and Voltages > 2-3 Purely Resistive AC Circuits
Chapter 2-3 Purely Resistive AC Circuits Resistance is defined as a parameter that causes a voltage drop directly proportional to the current that passes through it. That property is expressed as Ohm's Law. This effect holds equally true for both direct current (DC) circuits and for alternating current (AC or time varying) circuits. We earlier defined an instantaneous current to be where is the instantaneous current at any time and is the maximum value or amplitude. The quantity is expressed in radians per second and is the angular velocity. When that current exists in a simple series circuit the instantaneous voltage across the resistance is . In a purely resistive circuit voltage and current are in phase. This is indicated on a graph by showing the curves crossing the x-axis at the same points. For convenience of calculations, most often the origin is arbitrarily chosen as one of the crossing points. The equations just presented imply that condition. However, a different time origin is often necessary for many calculations. Given here that we consider the current to have a phase angle , these equations will look like this: and . That will cause the peak voltage to be .