Question
Download Solution PDFA current of 10 A flows in a circuit with a 30° angle of lag when the applied voltage is 100 V. What are the values of resistance and reactance in the circuit respectively ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
AC circuit with R-L load:
An AC circuit with an R-L load is shown below.
VR = Voltage across resistor
VL = Voltage across inductor
V = √(VR2 + VL2)
Total impedance is
Z = R + jωL Ω
Z = √(R2 + ω2L2) ∠θ
θ = tan-1(ωL/R)
Calculation:
Given
Current i = 10 A
Phase angle θ = 30° lag
Applied voltage V = 100 V
⇒ Impedance Z = V / i = 100 / 10 = 10 Ω
Impedance in polar form = Z ∠θ = 10 ∠-30° ('-' for lag)
Impedance in rectangular form = R + j XL = 10 cos 30° + j 10 sin 30° = 8.66 + j 5
⇒ R = 8.66 Ω and XL = 5 Ω
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