Why a complex term "j" is given with the capacitance value in a A.C circuit(simple practical explanation)
Why a complex term "j" is given with the capacitance value in a A.C circuit
Answer-
Answer-
What is a complex value or number? (3+j4) is a complex number, where 3 is put along the real axis and 4 along the imaginary axis.
j represents a 90 deg rotation in the CCW direction from the real axis
and -j will represent a 90 deg rotation in the CW direction from the
real axis.
Now consider an impedance consisting of a resistance of R=3 ohm and an inductive reactance of X=4 ohm (at 50 Hz). Connect this across a source of 5 V, 50 Hz, AC and measure the current it will be 1 amp and measure the voltage across resistance R, it will be 3 V and across reactance X(assumed ideal) 4 V. The current is same 1 amp through both R and X. the voltage drops RI and XI must add up to 5 V (not 3+4=7 but | 3+j4 |=5 ). this shows that you have to treat impedance as a complex number. Note that I have avoided rigorous mathematical details to keep the explanation simple.
Now consider an impedance consisting of a resistance of R=3 ohm and an inductive reactance of X=4 ohm (at 50 Hz). Connect this across a source of 5 V, 50 Hz, AC and measure the current it will be 1 amp and measure the voltage across resistance R, it will be 3 V and across reactance X(assumed ideal) 4 V. The current is same 1 amp through both R and X. the voltage drops RI and XI must add up to 5 V (not 3+4=7 but | 3+j4 |=5 ). this shows that you have to treat impedance as a complex number. Note that I have avoided rigorous mathematical details to keep the explanation simple.
By- Mohamed Rafeequdin,
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