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
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.
To find the rms value of the current in the circuit, we can use the formula:
I = V / Z
Where I is the rms current, V is the rms value of the voltage, and Z is the impedance of the inductor.
The impedance of the inductor can be calculated using the formula:
Z = 2πfL
Where Z is the impedance of the inductor, f is the frequency of the alternating emf, and L is the inductance.
Plugging in the given values:
L = 75mH = 0.075H (convert millihenries to henries)
V = 250V
f = 50Hz
Z = 2π * 50 * 0.075
Z ≈ 23.56Ω
Now we can calculate the rms current:
I = V / Z
I = 250V / 23.56Ω
I ≈ 10.61A
Hence, the correct answer is C. 10.46A