Numerical Problem 6, Alternating Current Circuit, Physics 12 … msa

admin November 2, 2020 Numerical Problem 6, AC Circuits 3 Comments

Problem 6: (a) Calculate the inductive reactance of a 3.00 mH inductor when 60.0 Hz and 10.0 kHz AC voltages are applied. (b) What is the rms current at each frequency if the applied rms voltage is 120 V.

Solution

(a) Given

Inductance, L= 3 mH = 3×10^-3H,
f₁ = 60 Hz,
f₂ = 10 kHz = 10 × 10³ Hz

Asked

Inductive reactance in both X_L1 and X_L2

Formula

X_L = 2πfL

Now put values for the first case, X_L1 = 2πf₁L = 2×3.14×60×3×10^-3 = 1130.4 × 10^-3 =1.13 Ω

Similarly, for second case, X_L2 = 2πf₂L = 2×3.14×10×10³×3×10^-3= 188.4 × 10⁰=188 Ω

(b) Given

V_rms = 120 V,
X_L1 = 1.13 Ω,
X_L2 = 188 Ω

Find

I_rms1, I_rms2

Formula: I_rms = V_rms/X_L

Now put values for first case, I_rms1 = 120/1.13 = 106 A

For the second case, I_rms2 = 120/188 = 0.637 A

Tagged Calculate the inductive reactance of a 3.00 mH inductor when 60.0 Hz and 10.0 kHz AC voltages are applied., Practice problem of alternating current circuit., Practice problem on calculating inductive reactance when when frequency of the current is given., What is the rms current at each frequency if the applied rms voltage is 120 V.

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