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PHY 102 Test Compilation PHY 102 17 Objective Question
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Question

A given RLC circuit has R = 100 Ω, L = 1H and C = 10μF (assumed, instead of 101F from OCR) all connected in series with a source of 200sin(ωt) with ω = 400 rad/s. Calculate the rms current.
Options
A 0.74 A
B 0.78 A
Correct Answer
C 0.72 A
D 1.11 A
Correct Answer

Option B is the correct answer.

Detailed Explanation

First, calculate the inductive reactance (XL) and capacitive reactance (XC):XL = ωL = (400 rad/s) * (1 H) = 400 ΩXC = 1/(ωC) = 1/((400 rad/s) * (10 × 10-6 F)) = 1/(4 × 10-3) Ω = 250 ΩNext, calculate the impedance (Z) of the RLC circuit:Z = √(R2 + (XL - XC)2)Z = √((100 Ω)2 + (400 Ω - 250 Ω)2)Z = √(1002 + 1502) = √(10000 + 22500) = √32500 ΩZ ≈ 180.28 ΩThe peak voltage (Vpeak) from the source is 200 V (from 200sin(ωt)).The RMS voltage (Vrms) is Vpeak / √2 = 200 V / √2 ≈ 141.42 V.Finally, calculate the RMS current (Irms) using Ohm's law for AC circuits:Irms = Vrms / Z = 141.42 V / 180.28 Ω ≈ 0.784 A.The closest option is 0.78 A.

Hint

Calculate inductive and capacitive reactances first, then the total impedance. Remember to use RMS voltage for RMS current calculation.

Question Info

Course: PHY 102
Topic: Test Compilation PHY 102 17
Type: Objective
Difficulty: Not specified
Question 1118 of 1819
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