Question
An inductor, L = 75mH is
connected in series to a source of
alternating emf of rms value 250V
and frequency 50Hz. What is the
rms value of the current? A. 21.22A
B. 1.69A
C. 10.46A
D. 5.31A
E. 26.53A
connected in series to a source of
alternating emf of rms value 250V
and frequency 50Hz. What is the
rms value of the current? A. 21.22A
B. 1.69A
C. 10.46A
D. 5.31A
E. 26.53A
Answers
GPT 3.5
The rms value of the current in an inductor can be found using the formula:
I = V/Z
Where:
I is the current
V is the voltage
Z is the impedance, given by Z = ωL, where ω is the angular frequency and L is the inductance.
The angular frequency can be calculated using ω = 2πf, where f is the frequency.
Substituting the given values:
ω = 2π(50 Hz) = 100π rad/s
L = 75 mH = 75 × 10^-3 H
Z = (100π rad/s)(75 × 10^-3 H) = 7.5π Ω
Now we can calculate the current using:
I = V/Z = (250V)/(7.5π Ω)
I ≈ 10.46 A
Therefore, the answer is C. 10.46 A.
I = V/Z
Where:
I is the current
V is the voltage
Z is the impedance, given by Z = ωL, where ω is the angular frequency and L is the inductance.
The angular frequency can be calculated using ω = 2πf, where f is the frequency.
Substituting the given values:
ω = 2π(50 Hz) = 100π rad/s
L = 75 mH = 75 × 10^-3 H
Z = (100π rad/s)(75 × 10^-3 H) = 7.5π Ω
Now we can calculate the current using:
I = V/Z = (250V)/(7.5π Ω)
I ≈ 10.46 A
Therefore, the answer is C. 10.46 A.