9.17. Draw and explain phasor diagram for voltage
and current in a purely inductive circuit.
Answers
Explanation and Derivation of Inductive Circuit
The circuit containing pure inductance is shown below:
pure-INDUCTIVE-circuit
Circuit Diagram of pure Inductive Circuit
Let the alternating voltage applied to the circuit is given by the equation:
PURE-INDUCTIVE-CIRCUIT-EQ1
As a result, an alternating current i flows through the inductance which induces an emf in it. The equation is shown below:
PURE-INDUCTIVE-CIRCUIT-EQ2
The emf which is induced in the circuit is equal and opposite to the applied voltage. Hence, the equation becomes,
PURE-INDUCTIVE-CIRCUIT-EQ3
Putting the value of e in equation (2) we will get the equation as
PURE-INDUCTIVE-CIRCUIT-EQ4
Integrating both sides of the equation (3), we will get
PURE-INDUCTIVE-CIRCUIT-EQ5where, XL = ω L is the opposition offered to the flow of alternating current by a pure inductance and is called inductive reactance.
The value of current will be maximum when sin (ωt – π/2) = 1
Therefore,
PURE-INDUCTIVE-CIRCUIT-EQ6
Substituting this value in Im from the equation (5) and putting it in equation (4) we will getPURE-INDUCTIVE-CIRCUIT-EQ7
Phasor Diagram and Power Curve of Inductive Circuit
The current in the pure inductive AC circuit lags the voltage by 90 degrees. The waveform, power curve and phasor diagram of a purely inductive circuit is shown below
INDUCTIVE-CIRCUIT-WAVEFORM
Phasor Diagram and Waveform of Pure Inductive Circuit
The voltage, current and power waveform are shown in blue, red and pink colours respectively. When the values of voltage and current are at its peak as a positive value, the power is also positive and similarly, when the voltage and current give negative waveform the power will also become negative. This is because of the phase difference between voltage and current.
When the voltage drops, the value of the current changes. When the value of current is at its maximum or peak value of the voltage at that instance of time will be zero, and therefore, the voltage and current are out of phase with each other by an angle of 90 degrees.
The phasor diagram is also shown on the left-hand side of the waveform where current (Im) lag voltage (Vm) by an angle of π/2.
Power in Pure Inductive Circuit
Instantaneous power in the inductive circuit is given by
PURE-INDUCTIVE-CIRCUIT-EQ8
Hence, the average power consumed in a purely inductive circuit is zero.
The average power in one alteration, i.e., in a half cycle is zero, as the negative and positive loop is under power curve is the same.
In the purely inductive circuit, during the first quarter cycle, the power supplied by the source, is stored in the magnetic field set up around the coil. In the next quarter cycle, the magnetic field diminishes and the power that was stored in the first quarter cycle is returned to the source.
This process continues in every cycle, and thus, no power is consumed in the circuit.
Anstry itwer:
Explanation: