Phase Difference between Current and Voltage in an AC Circuit

In an alternating current (AC) circuit, the current and voltage vary with time and can be represented by sinusoidal functions. The phase difference between the current and voltage waveforms determines their relationship and is an important parameter in understanding the behavior of the circuit.

Given Equation:
I = I0 sin(wt)
E = E0 cos(wt + π/3)

Where:
I is the current in the circuit
E is the voltage in the circuit
I0 and E0 are the maximum values of current and voltage respectively
w is the angular frequency of the AC signal, given by 2πf (f is the frequency in hertz)
t is the time

Analysis:
To determine the phase difference between the current and voltage waveforms, we need to compare their respective arguments in the sine and cosine functions.

Current Equation:
I = I0 sin(wt)

Voltage Equation:
E = E0 cos(wt + π/3)

The angular frequency (w) is the same for both the current and voltage waveforms, indicating that they have the same frequency. However, the phase difference is determined by the additional phase shift term (π/3) in the voltage equation.

Phase Difference Calculation:
To calculate the phase difference, we need to compare the arguments of the sine and cosine functions. In this case, the argument of the sine function is wt, while the argument of the cosine function is wt + π/3.

Since the argument of the cosine function (wt + π/3) is ahead of the argument of the sine function (wt), we can conclude that the voltage waveform leads the current waveform by a phase difference of π/3 radians or 60 degrees.

Conclusion:
The phase difference between the alternating current and voltage represented by the given equations is π/3 radians or 60 degrees. This means that the voltage waveform leads the current waveform in the circuit by 60 degrees. Understanding the phase difference is essential in analyzing AC circuits and determining their behavior.