The virtual current of 4A and 50Hz flows in an AC circuit containing a...
Given Information:
- Virtual current: 4A
- Frequency: 50Hz
- Power consumed: 240W
- Virtual Voltage: 100V
Calculating Resistance:
As we know:
Power = (Virtual Current)2 x Resistance
Therefore, Resistance = Power / (Virtual Current)2
Resistance = 240W / (4A)2
Resistance = 240W / 16A2
Resistance = 240W / 256
Resistance = 0.9375 ohm
Calculating Inductive Reactance:
As we know:
Inductive Reactance (XL) = 2π x Frequency x Inductance
Therefore, Inductance = XL / (2π x Frequency)
Virtual Voltage = Virtual Current x Impedance
Impedance = √(Resistance2 + XL2)
Virtual Voltage = Virtual Current x √(Resistance2 + XL2)
100V = 4A x √(0.93752 + XL2)
25 = 0.93752 + XL2
XL2 = 25 - 0.93752
XL2 = 24.94
XL = √24.94
XL = 4.994 ohm
Calculating Inductance:
Inductive Reactance (XL) = 2π x Frequency x Inductance
Therefore, Inductance = XL / (2π x Frequency)
Inductance = 4.994 ohm / (2π x 50Hz)
Inductance = 0.0159 H
Final Answer:
The resistance of the coil is 0.9375 ohm and its inductance is 0.0159 H.
Option D) 1/π ohm is not the correct answer.