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When a sinusoidal voltage is applied across RL parallel circuit so that R = XL the phase angle will be
45┬░ lagging
45┬░ leading
90┬░ lagging
90┬░ leading
45┬░ lagging
In a parallel RL circuit, the total current I lags the applied voltage V by an angle ╧Х. Since the resistor and inductor are connected in parallel, they share the same voltage V, and the circuit impedance involves the ratio of the resistive current IRтАЛ=RVтАЛ and inductive current ILтАЛ=XLтАЛVтАЛ.
In a parallel RL circuit, the total current I lags the applied voltage V by an angle ╧Х. Since the resistor and inductor are connected in parallel, they share the same voltage V, and the circuit impedance involves the ratio of the resistive current IRтАЛ=RVтАЛ and inductive current ILтАЛ=XLтАЛVтАЛ.
╧Х=тИТarctan(XLтАЛRтАЛ) тАФ Phase angle of parallel RL circuit
I=IR2тАЛ+IL2тАЛтАЛ тАФ Total current magnitude
The total current in a parallel RL circuit is given by I=IRтАЛтИТjILтАЛ. The phase angle ╧Х is defined as ╧Х=тИТarctan(IRтАЛILтАЛтАЛ). Given R=XLтАЛ, then ILтАЛ=XLтАЛVтАЛ=RVтАЛ=IRтАЛ. Substituting these into the formula: ╧Х=тИТarctan(V/RV/RтАЛ)=тИТarctan(1)=тИТ45┬░. The negative sign indicates a lagging power factor.
In parallel circuits, voltage is the common reference.
Inductors cause the current to lag behind the voltage.
When resistance equals inductive reactance, current magnitudes are equal, leading to equal real and reactive components of the total current.
A phase angle of 45┬░ indicates a power factor of cos(45┬░)=0.707 lagging.
Easy to determine phase using current components
Voltage remains constant across parallel branches
Total current increases as frequency decreases
Does not reach resonance like RLC circuits
Induction motor modeling
Transformer equivalent circuits
The phase angle ╧Х is the angle between the total current and the reference voltage.
Option B (45┬░ leading) is incorrect because inductors never lead voltage.
Options C and D are incorrect as 90┬░ only occurs in purely inductive or purely capacitive circuits.
A is correct тАФ The phase angle in a parallel RL circuit with R=XLтАЛ is 45┬░ lagging because the resistive and inductive current components are equal in magnitude.
Always remember: in Series RL, tan(╧Х)=RXLтАЛтАЛ, whereas in Parallel RL, tan(╧Х)=XLтАЛRтАЛ (with a negative sign for lagging current).