IMPEDENCE

Submitted by

Gopi chand

IMPEDENCEo In an electrical circuit the impedance of a

component is defined as the ratio of the voltage phasor v, across the component over the current phasor I , through the component.

The impedance phasor for the capacitor, inductor,and resistor are summarized in table below

Positive phase occurs when the phasor is rotated in the counter clockwise direction beginning from the positive real axis

When the phasor is lined up with the positive imaginary axis (vertically upward) 90° of the phase has been accumulated.

When the phasor is pointing leftward,180° of the phase has been accumulated.

When the phasor is pointing downward along the negative imaginary axis, 270° or -90 ° of the phase has been accumulated.

Keeping in mind that impedance is voltage divided by current, a positive imaginary component indicates voltage leading current, and a negative imaginary component indicates voltage lagging current.

Because j occurs in the denominator of the capacitor impedance, the capacitor voltage lags its current by 90°.

Similarly, because j occurs in the numerator of the inductor impedance, the inductor voltage leads its current by 90°.

Consider the sinusoid x(t) = sin ωt . If we differentiate x(t) analytically with respect to time, we obtain

X ‘(t) =d(sin(ωt))/dt = ω’cos(ωt) Further more, since cos λ = sin(λ + 90°)ω ,

the right side of X ‘(t) may be written as ω‘ sin(ωt + 90°) or simply jω’ sin(ωt)

This means that differentiation of a sinusoid of frequency ω is the same as multiplication of the sinusoid by j ω .

The impedance of a component is often represented as ZX, where X is the component name or description.

In terms of the potential and flow variables, the impedance of a component is defined as the ratio of the potential variable to the flow variable

1

For example, consider the circuit element shown in Figure

In accordance with Equation 1, the impedance of the circuit element becomes

Z = PV1 - PV2/FV

=ΔPV/FV