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Equation of current in vector method is
I=RVтАЛ
I=YXтАЛ
I2=X2+Y2
I=XтИТY
I2=X2+Y2
In an A.C. parallel circuit, the total current is the phasor sum of the branch currents. According to the vector addition rule for orthogonal components (like active and reactive currents), the magnitude of the resultant current is found using the Pythagorean theorem, represented as I2=Ia2тАЛ+Ir2тАЛ.
In an A.C. parallel circuit, the total current is the phasor sum of the branch currents. According to the vector addition rule for orthogonal components (like active and reactive currents), the magnitude of the resultant current is found using the Pythagorean theorem, represented as I2=Ia2тАЛ+Ir2тАЛ.
I=Ia2тАЛ+Ir2тАЛтАЛ тАФ Magnitude of total current
I2=X2+Y2 тАФ Pythagorean relationship for orthogonal currents
In A.C. circuits containing resistance (R) and reactance (X), the current components are in quadrature (90┬░ apart). The total current I acts as the hypotenuse of a right-angled triangle where the horizontal base is the active (in-phase) current and the vertical height is the reactive (quadrature) current. Consequently, the square of the resultant current equals the sum of the squares of its orthogonal components.
A.C. currents cannot be added algebraically unless they are in phase.
The vector method accounts for the phase difference between resistive and reactive branches.
This concept is fundamental for calculating the power factor and total impedance in complex networks.
Provides an accurate resultant magnitude for out-of-phase components.
Simplifies complex circuit analysis using right-triangle trigonometry.
Only applicable for orthogonal (90┬░) components.
Requires knowledge of phase angles for non-orthogonal current additions.
Power system analysis for inductive/capacitive loads.
Calculation of total line current in parallel R-L and R-C circuits.
In the context of the question, X and Y represent the orthogonal components of the total current I, typically the active current (Icos╧Ж) and reactive current (Isin╧Ж).
Options A, B, and D are incorrect as they do not represent the magnitude of a resultant vector involving quadrature components.
C is correct тАФ The equation I2=X2+Y2 represents the Pythagorean relationship for the magnitude of a resultant phasor composed of two orthogonal components X and Y.
Always verify if the components are in phase or quadrature before applying addition rules; algebraic addition applies only to in-phase components.