Alternating Current

Peak Value and RMS Value of Alternating Current

1. Peak Value ( )

The peak value of an alternating current (or voltage) is the maximum value attained in either direction during one cycle. It is also called the maximum value.

Definition: The highest point reached by the AC waveform during a cycle.

2. RMS Value ( )

The root mean square (rms) value of an alternating current is defined as the value of a steady (DC) current that would produce the same amount of heat in a given resistor in the same time as the AC does.

Mathematical Relation:

The RMS value for current is related to the peak value as:

Similarly, for voltage, the RMS value is related to the peak voltage as:

Conclusion:

The RMS value is particularly useful because it represents the effective value of an alternating current or voltage, which can be directly compared to a DC value in terms of its ability to produce heat in a resistor.

Magnetic Flux and Induced emf vs Time

Consider a square loop moving with a constant velocity through a uniform magnetic field region. The magnetic flux and induced emf vary over time as the loop enters and exits the field. Let’s define three distinct intervals:

• From to : The loop enters the magnetic field.
• From to : The loop is entirely inside the field.
• From to : The loop exits the magnetic field.

Magnetic Flux vs Time

• From : The magnetic flux increases linearly as the loop enters the magnetic field. As the area of the loop inside the magnetic field increases, so does the flux.
• From : The magnetic flux remains constant as the loop is fully inside the magnetic field.
• From : The magnetic flux decreases linearly as the loop exits the magnetic field. As the area of the loop inside the magnetic field decreases, the flux decreases.
• For : The magnetic flux becomes zero as the loop is completely outside the magnetic field.

Induced emf vs Time

• From : The induced emf is constant and non-zero. The change in magnetic flux induces a constant emf.
• From : The induced emf is zero, as there is no change in flux while the loop is fully inside the field.
• From : The induced emf is constant but opposite in sign, as the flux decreases while the loop exits the magnetic field.
• For : The induced emf becomes zero, as there is no change in flux once the loop is outside the magnetic field.

Summary:

The magnetic flux and induced emf change in a predictable pattern as the loop moves through the magnetic field:

• Magnetic Flux:
• Induced emf: